There's nothing wrong with that camera or lenses, but for probably $800, you can get an outfit much more suitable for your needs.
Little kids. Lots of your shots will be indoors with a wide lens (55mm or less). The onboard flash will make any camera take crappy point and shoot looking pictures. You either want a fast prime lens (a 35 or 50mm at f/2 or less should run around $150'ish) which will allow you to skip the flash and/or a speedlight. A speedlight is a flash that mounts on top that you can point around, allowing you to bounce the light and fill in ugly shadows. Those aren't too expensive either.
That longer lens might not be something you use a lot, and if so, you should be able to pick one up for around $150.
Camera bodies depreciate terribly. I would highly recommend picking up something used that is 1 or 2 generations old. You might miss out on some of the small conveniences of the latest and greatest, but you can put that savings into gear which actually holds value--glass and a speedlight. If you look back a year from now and realize you haven't used it more than a handful of times, you can sell the whole match for pretty much the same that you paid for it. Pretty much any body built going back 10 years will deliver the images you want.
KEH is a great place for used lenses and bodies. I haven't bought anything new in a long time.