With two kids sounds like fun. With a dog? No way.
With just the kids you can pull over when you see something interesting and explore, stop at restaurants and bowling alleys and swimming pools and movie theaters when you need a break midroute, and switch to a new hotel if you get tired early. With a dog you can't do anything indoors along the way.
Of course, my version would probably still cost you $2000 in movies, restaurant meals, hotels, gas, etc . . .