Truthfully, your planned trip is too many miles in too few of days. If your children are just out of booster seats then they're very young. Subjecting them to this long drive along with your mother in one seat in the truck would be very confining. The drive itself is hot and boring.
With an RV you do not make time like you do in a car. It's wise not to go over 65 mph. You have approximately 1600 miles each way and I would estimate a good long day would take 3 days.
From Williams to Bryce is 300 slow miles, not 3 hours as you estimate.
Even if your wife could help drive you still have the three passengers to think about. Also, if your wife thinks she can drive a motorhome then she can also tow a trailer just as well, especially on the interstates.
Your children are still young to really get a lot out of these two places. Would you have a two-week vacation the following year that you could have more time for enjoyment?
You also have to take into account of illnesses or mechanical problems along the way. Having some extra days would help out.
You need time to find the right RV and two months is rushing it. I don't know....to me it's just too rushed.