Couple of thoughts...to take with a grain of salt as I'm just some dude on the internet.
I know you're asking for advice on fixing what's already happened, but it's helpful to know that the lighting conditions were setting you up for this challenge to begin with. Of course, we can't always choose when and where we shoot! That being said...
1. Even with adjustments, detail in the white bow isn't recoverable -- it's burned (at least in the JPEG). This is a product of the harsh light. Looking at the shadows, I'd guess this was shot somewhere around 10-11AM or 3-4PM -- definitely unforgiving light.
2.) I know it seems counter-intuitive in bright light like this, but fill flash would be one way to tackle the challenging light (one reason why I still like pop-up flashes). You can bring your exposure down to tame the harsh sun and then fill with an appropriate amount of light. Easier said than done, though, when you have a baby turning into the sun, then away from the sun, then back into the sun!
3.) Another option, if you have someone to assist you, is to use a diffuser of some kind to soften the light (even a white bed sheet would probably work). That would take the edge off the highlights, allowing more recovery of detail.
Since you're working with a JPEG file, you're a lot more limited in what you can do to correct things like exposure and white balance. Jim demonstrated well how much you can improve the file from what it is, but I'm confident it could be improved much further from a RAW file. That being said...
1.) The next thing to correct after the exposure/highlights is the orange glow (kind of like banding) that is visible along the middle and sun-edge of each arm and at a 45 degree angle on the sunlit cheek (this can happen in sunset images, too). You might need to use a brush or layer to tone down the saturation. The challenge is that you can't just bring down the orange, or the rest of the skin will look pale and sickly. If this was a RAW file, it might be possible to desaturate the orange channel and then adjust color temperature to bring back the warmth (you'd have to do that locally, though, so as not to spoil the white balance of the whole image.
2. I'm curious to know what it is about RAW that doesn't work for you. When I first started dabbling in RAW processing, I was using Digital Photo Professional. I found it difficult and tedious, and I struggled to get results that were better than the JPEGs coming from my camera (although the CA correction was very nice). Lightroom, on the other hand, is much easier, in my opinion, and more powerful. I really enjoy using it, and my processing results have improved. With a few good tutorials on YouTube, you can get a good start. If you haven't yet tried Lightroom, you might consider it.
3.) Just to beat the RAW vs. JPEG horse some more (I thought I saw it twitching still), the camera makes white balance, contrast, noise, sharpening and other decisions for you, baked into the image. In this case, it looks like it sacrificed highlight detail for shadow detail. You can see the shaded side of her face okay, but her bow and sunlit skin are fried. With a RAW image in Lightroom, you could selectively bring down highlights to recover any detail that's there while still boosting the shadows as necessary. Local adjustment brushes give you even more flexibility.
Anyway, I hope this is helpful, and I apologize if you already know or have thought of all this stuff. Maybe it will be useful for someone else.
By the way, if you have a RAW file for this image, I'd be interested to see how much more pushing/pulling can be done.