Over and above Michael's well worded comments.... if you are driving even 500 miles per day with a child and have to set up camp and pack up camp each day, you are going to be exhausted before you have even got a fraction into your trip. The two year old deserves more consideration than you are presently planning. (Most of us here have travelled with small children and are only too aware of their needs over a multi day roadtrip.)

Even following the advice above, is far too much for an enjoyable camping trip with your family.

Lifey