HELP!!! Trip planning

I agree that is a very aggressive plan but you could do it.
Days 1-5 travel; days 6-8 Canyon; days 9-14 travel.
Long 8 hour driving days, no time to see anything in between home and Canyon.
Not a fun trip in my opinion but definitely doable.

Change the plan. It's too far and, unless you hike, too little time is spent at the South Rim. The average is three hours!
Don't know the details of you family makeup but if you have kids I'd go instead to Cedar Point in Ohio which is the roller coaster capital of the world.
Isn't the football hall of fame in Ohio and the rock n roll hall?
Go the other way to the west end of the Erie Canal and take a boat ride out of Lockport.
You could even drive to Springfield, IL and visit the Lincoln Museum. It's good for half a day at least. His tomb is there also. Some parts of the old Route 66 are there. Have a corn dog at the Cozy Inn.
When in doubt do a Google search for `______ tourism' and put the city, state or area in the blank space. You might even put Pittsburgh in there. BTW why is there an `h' at the end of Pittsburgh?

Reservations for the Grand Canyon is a must of course. That is a long drive and with 10 days, youll spend most of it driving back and forth, so google the fastest route, get there and spend as much time as you can before you turn around and go back (Driving an 8 hour day is pretty harsh in an RV/or pulling a trailer.)