>"I will spend up to $850 if its a DSLR"
That's a little low unless you're talking body only.
>"A little worried about it being large and having to carry it around with kids and all the other stuff that goes along."
That's exactly the situation that the micro 4/3 system was designed for--interchangeable lenses with near DSLR quality in a smaller package.The newest model is Panasonic's GX1, and Olympus should announce a new (OM-D?) model in the next week or so.
There's also Sony's NEX line, but be sure to factor in the size of the lens in addition to the body. Although, for indoor (family) candids, you should be able to use the 16mm f2.8 "pancake".
Or if you can double your budget--not likely, I know, but just in case--there's Fuji's X Pro 1.
Or if you're willing to spend your $850 DSLR budget on a fixed lens (point-and-shoot) with a large (near APS-C size) sensor, there's Canon's G1X.
HTH - Mark
I want to get a better camera to take pictures of the family and I am thinking it might be time for a DSLR. A little worried about it being large and having to carry it around with kids and all the other stuff that goes along.