If you can't hand-hold a DSLR and manual focus the 50 1.8 with one finger, your skill level doesn't warrant handling anything more expensive if you ask me. Moving up to the 1.4 is a marginal improvement for a 3x price difference... and getting into that price range, you might as well invest in a slightly more expensive Tokina 11-16
If you're spending as much as $500, I would DEFINITELY recommend the tokina 11-16 2.8. At infinity focus, everythign a meter out or farther will stay in focus. For filming kids, wide and already in focus should be a big plus for convenience factor. Not missing a memory is more important than bokeh quality
?! The tiny amount of travel on the 50 f1.8 makes manually focussing ACCURATELY very hard. The lens is blatantly not designed to be manually focussed, and doing so is a pain in the ass. By contrast the 50 1.4 has over 360 degrees of travel meaning that you have far more fine grained control over focussing. That isn't a marginal improvement, its the difference between useable and not.
And suggesting a UWA as an alternative to a 50mm prime is just bizarre. Unless you want the extreme perspective distortion that comes with a UWA lens (great for landscapes/cityscapes/particular look how enormous my nose is portraits - crap for any kind of close up) this is awful advice.
For the use that the op suggested the tamron 17-50 2.8 (with or without VC) is a far better choice for less money.