Thank you all.
Having read (a lot) about my options, I've come to the conclusion that shooting hyperactive kids in low light conditions but having a camera I'm actually likely to use a lot and bother getting out of the drawer = Sony A6000. So that's what I'm going to buy.
My poor wallet.
I wouldn't buy a mirrorless camera for tracking anything in low light conditions, the cheapest SLR's focus better.