191 south to 160 to 89 south to Cameron, AZ then 64 west into the park is the way you'd want to go if staying at Trailer Village in the park.
If you're staying in Williams you could take 89 into Flagstaff and west on I-40.
The above is very good with your 40' MH. We've done it often.
You will also be passing by Monument Valley if you've never been there. The only RV park is Gouldings - nice views. Take a tour of Monument Valley or drive your towed vehicle if it's suitable. 4x4 isn't necessary but a high clearance would be ideal.
Have a good trip!
Full-timed for 16 Years . . . Back in S&B Again
Traveled 8 yr in a 2004 Newmar Dutch Star 40' Diesel
& 8 yr in a 33' Travel Supreme 5th wheel