It sounds like you're chasing medium format ("bigger sensor with more DR"), mirrorless (eye detection, lighter), and action SLR ("kids sports") all in one... and that really doesn't exist.
A little background info so you know where I'm coming from and my advice has context: I use everything, and I do mean everything. Canon, Fuji, Sony, Nikon, Phase, Hasselblad, Mamiya, Rollei. Panasonic now and then. All small formats, a few medium formats, and a couple of large formats, analogue and digital; hell, I used to even offer plate shooting. My primary work is very intensive archival and cataloguing for a few specific corporations, which involves many of the same techniques as landscape (maximising resolution and dynamic range, pixel-perfect stitching, viewing at 1:1 or very large print, etc), and conversely as a hobby I try my hand at a little wildlife photography (so there's your low-light speed shooting); over the years I've done a bit of everything from the most basic amateur portraits to music to documentary for the BBC. I'm not terribly old but it's fair to say I have a helluva lot of experience anyway. I'm not perfect and absolutely nobody's taste and needs will ever line up perfectly with your own, but suffice to say I consider myself pretty well versed in switching between systems and I don't have any particular horse in this race.
Though, full disclosure, I do use Canon just a little bit more than the others; it's hard to beat the sheer depth of the Canon lens selection. As it happens my favourite Canon lenses are the 70-200 f/4L IS and the 100mm f/2, and I have a certain fondness for the 35mm f/2 IS and 17-40 f/4 even though they don't feature in my work often, so hey, we've got those in common.
Okay, with that out of the way.
Right now, a bigger sensor and more dynamic range means getting a medium format system. Frankly, if you can afford a medium format system, you probably wouldn't even have made this thread. Medium format isn't something anybody switches to casually. Either you need it and can get it and you know it... or it's not even remotely on the cards for you. Think hard about whether you can—let alone would want to—make that jump. Medium format cameras will certainly give you that step up in image quality for your big landscape prints, but they're very expensive and very, very slow. You'd want to keep your Canon gear in order to keep doing your sports shooting.
Ditching the idea of a bigger sensor and trying to keep you to one system, you could try the Nikon D850. It's got better dynamic range than any Canon and more resolution—without the detail-destroying low-pass filter—than your current 5D3. It's also got incredibly good AF and shoots very, very fast. Nikon's live view shooting isn't so great, so you don't quite get that perfect eye detect of a mirrorless system, and it's not a small or light camera by any means, but it does do everything else, so there'd be no need to maintain a second system like you would need if you got into medium format. I've been playing around with one for a week now and it's hard to not add one to my personal kit. It's faster than any Canon except the 1DX2, the AF is—at the time of writing—the very best I've ever seen in any system, and the image quality is as good as it gets for a 35mm sensor.
I've yet to get my hands on a α7R3 yet, but for what it's worth, it's the first Sony body I've not been terribly excited for. It's great on paper, but the α9 is still categorically faster (that's the whole point of the α9) and the rest of the α7R3 doesn't seem to offer enough over the D850 for me to feel it's worth having both, especially with Sony's sketchier lenses; Sony have improved their lenses a little, but with the α7R2 I still get better (from a purely technical point of view; there's no accounting for personal taste) results with Sigma, Tamron, and adapted Canon lenses than any Sony lens. Having used the D850 and used the other Sonys enough, I'm finding it very difficult to care about the α7R3. The α9 is a helluva machine, if the fastest speed and best AF in the smallest package is something you're interested in. I can see a lot of people picking up both the α9 and the α7R3 so they have one camera for speed and one for image quality. But if you don't want to pay out for two bodies then Sony is a bit of a tough sell. If you'd said you were doing a lot of video then I'd recommend Sony right away, because that's a big strength of theirs, but landscape and indoor sports? Not so much.
If you've been tempted by the 5DS R but are worried about speed, again I'd suggest considering having two bodies. The 5DS R for big print quality and something like a 7D2 for speed (though the 7D3 should be coming within the next 12 months) is a great combo, and though having two bodies may seem like a big investment, buying two Canons at least means you can keep using the same lenses, which will in most cases work out cheaper than switching to another brand.
I will suggest that if you're finding your 5D3 can't keep up with kids' sports, something is either mechanically wrong with the camera, it's not set up well for the task, or you're plain doing something wrong. The 5D3 has absolutely minimal shutter lag and a great AF system; I've yet to find any mirrorless camera which locks focus faster, so if keeping up has been a problem for you with the 5D3, any mirrorless body is going to disappoint you.
Really, the main problem I see with your kit you list is you're using f/4 zoom lenses, which are always going to be that touch slower to focus in lower-light situations (e.g. indoors) than if you have any of their f/2.8 equivalents, let alone much faster primes. I like the Canon f/4 zooms myself 'cause nothing I do ever requires that very shallow depth of field of faster lenses and the f/4 zooms are a reasonable weight, but there's no mistake that when I need speed, I get out the f/2.8 zooms or specialist primes.
For what it's worth, I've had a 5D2 (yes, 2) keeping up with a lanner falcon—which moves at around 85-110mph and is only about 2'x3', so far smaller and faster target than any 12-year-old!—when using the 300mm f/2.8, while the 300mm f/4 has struggled even on a 1DX body. That one stop really does make a lot of difference to AF speed; the more light you can get inside the camera body, the better AF will be, always; it can be absolutely vital when shooting indoors. Moving to the 70-200 f/2.8 IS could be enough to solve your speed problems (and it's a touch sharper than the f/4, to boot) and should be cheaper than switching systems. Consider renting one to see if a lens upgrade is actually all you need. The same goes for the wide-angle and standard zooms. It really is also worth thinking about whether your settings & technique could be improved, too, because a 5D3 really should be able to keep up with any sports requirements, even with the f/4 lenses being a touch slower.
A last note, almost regardless of whether you switch systems or not, is to look at third-party lenses. The current Sony 24-105 isn't as good as the Sigma 24-105 (and the new Sony is pitched as a lower model, so that won't be any better), and in fact neither is the Canon 24-105. There's also things like the Tamron 24-70 f/2.8 VC which absolutely destroys all the 24-105s when used at f/4; Canon is thought to be making their own 24-70 f/2.8 IS, but that one will certainly be a lot more expensive and there's no telling when it'll come out (if it ever does). The general rule across their ranges is that Sigma's optics beat everyone other than Zeiss, but their AF can be inconsistent; Tamron have perfectly accurate AF but it's a touch slower, and their optics aren't quite as good as Sigma (though still better than most Canon, Nikon, and Sony first-party lenses). So whether it's a lens upgrade for your current body or a new lens for a new system, it's really worth keeping those third-parties in mind. A Sony body and Sony's 24-105 isn't really that great a swap, but a Sony body and the Sigma 24-105 is a helluva all-round combination. (In fact Sony are especially good for it, as being mirrorless eliminates the slight AF accuracy inconsistency some Sigmas can have.)
So, to summarise:
- First think about whether a simple lens upgrade and/or a second Canon body could fill in what you're missing. This will be cheaper than switching brands entirely.
- If that's not enough, try to be realistic about your expectations and needs; there's no such thing as one camera which has all of a bigger sensor, better IQ, lighter weight, and more speed. You will have to give up [/i]something[/i], or use two bodies/systems to cover it all.
- For a single body, the Nikon D850 comes closest to fulfilling what you ask for. It's not a bigger sensor but it's got everything else.
- The Sony α7R3 seems very good but always be wary of jumping on the latest hottest product; you don't yet know what (if any) problems they might have and it's easy to get swept up in the hype. Again, even as someone who likes the Sonys a lot, I can't say it's exciting me like the D850 has already proven. I'm very sure it would make a great second body, though, as the α7R2 already does.
- Canon is expected to put out quite a few new products over the next 12 months or so, such as the 7D3 for sports, so it might be worth you waiting to see what turns up; if you've waited 12 years, another 12 months isn't going to kill you.
- Medium format + a fast SLR or Sony α9 would achieve everything you want, but will also be by far the most expensive option. Keep it in mind, but try to not get too fixated on the idea unless you're really willing and bale to go all-in.
- Whether you switch or stay, keep those third-parties in mind; for landscapes, especially, you might find one of the ultra-sharp Sigma lenses is a better upgrade for you than a body swap. Switching systems can be really expensive and it's always disappointing if you switch expecting a big improvement and you end up with pretty much the same results (especially with Sony, where the sensors are great but the lenses are decidedly average); third-party lenses can solve both the quality and cost issues associated with swapping systems.
- No matter what, rent everything before you make any big decisions. Swapping systems always winds up costing more than you will think yet doesn't always change your results much, so a couple extra hundred to try everything out for a week or so before hand so you're absolutely sure it's right for you can be absolutely worth it.
Take it from someone who would really, really like to be able to scale down and work with just one system: hopping back-and-forth like this is a big pain for very little gain. Do not overestimate the results and do not underestimate the hassle. I'd hate to see someone waste time and money switching systems if it won't actually deliver what they expect. There's certainly a lot of things other systems can do better than your current Canon gear, but everything is always a trade and a compromise. Think carefully, think hard, and take your time.
