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There are a few basic rules of thumb that, if you heed them, will make your trip much more relaxed and worry free. The first is to remember that everywhere is somebody's hometown. Yes, there are 'bad' neighborhoods, but you'll easily recognize them - just as you do in your own city. Your own radar is your best advice on when you should simply move on from an area. Next, it is best to measure the length of trips this involved in days, not hours. Houston to Boston at a relaxed pace and taking minor detours to avoid large urban areas is going to take four days. That will put you on the road for about eight hours a day including meals and some play breaks for the children. And as far as the kids go, at that age they don't need much to amuse them. Simple parks and playgrounds will do just as well as expensive entertainment sites. So just plan on stopping every 2-3 hours to give them some run-around time.
Now, a route. You are fortunate that the shortest all-Interstate route also does a pretty good job at avoiding major metropolitan areas, particularly in the mid-Atlantic region. I-10/I-12/I-59/I-75/I-40/I-81/I-84/I-90 will get you to Boston while missing Atlanta, Washington and New York. Taking four equally paced days would have you spending your nights in Laurel ms. Knoxville TN, and Harrisburg PA. Each of those will offer you plenty of accommodation choices.
AZBuck