Like others have said, I’d recommend a mirrorless camera over a DSLR, especially if you’re taking photos of kids. I’ve recently switched from a Pentax k-x DSLR to a Sony a6000 mirrorless. One of the main reasons I switched was for the burst speed of a mirrorless.
This means that if the kids are running around like lunatics, I can set the burst mode to high, and it takes 11 photos a second, for a bit over two seconds. I’ve got a much higher chance of catching them with their eyes open, or not pulling a face as they’re moving, and so on. With a decent sized memory card you can take thousands of photos, and just delete the ones you don’t like.
The camera is a lot lighter too, and the lenses can be smaller, so they’re easier to carry and to use hand held.