Entry level DSLR camera to shoot kids, pets, and action shots?

I'm looking to get into photography and want to stay under 1000.00 dollars. My main focus is kids and pets. I'm also hoping for some great night shots as well. I've been reading a lot on canon and nikon and reviews differ so I'm hoping somebody who actually owns a camera like what I'm wanting can offer up a good opinion. I don't care about video, I just want to be able to catch animals and kids playing without much worry. Again easy settings for night shots are a plus too.

Any number of entry-level DSLRs will serve you just fine.
I prefer Canon models, and would suggest either the Canon T2i or T3i. You could get either with the kit lens plus an additional decent lens for under $1000.
But a number of the Nikon entry-level models will do just as well.
Go to a camera store, try out some of the models, and get the one that feels best to you.

Rebel T3 or Nikon D3100. Those will both leave you with some extra $$$ to put towards a nice lens or two.

Nikon D3100.

A Nikon D5100 with kit lens will fit within your budget. Add an SD card and a good tripod, and there goes the rest of your budget. Add more money, and you can add a flash and telephoto zoom lens.