I looking to invest in a camera that takes pictures of kids, moving kids very well. I have a 1.5 year old that is nothing bu

Anything with a fast shutter will do the trick. Any DSLR will do just fine for sure, otherwise if you're looking at more basic cameras, just look for something with a fast shutter speed and you'll be very happy with the results.
 
What is your budget? Do you want interchangable lenses? Is size a consideration? By your use of "photographing", I assume you mean still photos and not videos, is that correct? How much of a concern is rain and dirt (is weather resistant a REQUIREMENT)?
 
all depends how much you villing to pay,cause technology in this days endless,like waterproof(using on the seaside dont worry sand get in to)project from device on the room wall what you just get on the camera.