MDB, you're not like any family I know if you have 4 kids a full time job and have time to drive x country multiple times a year to visit family.
We drive ALOT and the few trips back to the midwest (shorter than your proposed trips by probably 500 miles) are 2 days of driving basically straight through, 3 long days in the car or 4 days of "normal" drive 500-600 miles a day.
Your proposal is to spend basically a week in transit to go back to visit for how long?
Driving slower and exercising more caution, more things to go wrong, $1000 extra in fuel, extra wear n tear on the truck, 6 bodies packed into a vehicle for basically 25% longer than if running bobtail....
Yes, $ for $ you could do it cheaper that way than buying 6 plane tickets, rental car a week's worth of hotels in NY (2 rooms?), but dayum.....
Think about the cost of the RV, how many times you'll make the trip, how much time you have to spend behind the wheel and pencil it out.
And if your kids are 8-16 years old or whatever you said, how many times will you have the time to take 2-3 weeks and not interrupt any of the 6 family members' schedules? And will this be your family vacations or do you actually have more time to take family vacations on top of these trips?
Our kids are 13 and 16 this year and thus far, there's been less than 10 weekends total in the last 12 months that there aren't multiple kid or parent commitments.
Think you'll come to the realization that this plan will not yield alot of trips back east. And if those folks wanted to see you that bad, they could come to you. Quite likely some/many of them can travel lighter/easier/cheaper than you with 4 kids and if they're like my family they can't afford it or won't/can't take the time anyways.
The cheapest option is for you to pay to fly both sets of grandparents out to see YOU when needed, honestly.
JMO, because we are in the same situation as you for the last 20 years and kinda been there done that.