For me, the height mentioned in the OP eliminates the NYS Thruway from your choice of route. The Western end of the Thruway has many bridges rated at 13' 6", with warning signs. Since the 13' 4" mentioned is a static height (not moving down the road) I'd stay away from the Thruway. I notice your in Vermont, so there are choices of westward routes.
I am not a fan of the Detroit, Cleveland and Erie area. For me, it is an area to get through as quickly/safely as possible.
Consider taking I88 to I86 across NYS. In Jamestown, NY there is the Lucille Ball museum. Go to Lucille Ball 100th Birthday August 6 | Lucille Ball - Desi Arnaz Center
and read about it.
If you stay on I80/I90 through North Eastern Indiana, there are quite a few RV manufacturing plants in the area. Shipshewana, IN is a few miles south of I80/I90. Between Shipshewana and Nappanee, IN is Amish and RV country. Newmar is in Nappanee. Plant tours are offered 2 times a day. I like what skigramp posted about going north through the LP and UP of Michigan. The northern part of the LP has Sleeping Bear Dunes National Lakeshore. Then, northward to the Mackinac area. Continue on North to the American side of Sault St. Marie. There is a Great Lakes Maritime Museum (inside a ship). One can also take a boat ride through the locks.
Then go west young man go west. The shopper in your family will like the next stop. Consider stopping at the Mall of America in Minneapolis, MN.
Since you've been to the western area before I'll confine my suggestions to some things you might not have done.
Minuteman Missile National Historic Site at I90 exit 131. Go to Minuteman Missile National Historic Site (U.S. National Park Service)
and read about it. Reservations are a must. Same exit, go through the Badlands National Park and stay at the Badlands KOA. Around dark, go the the NP Amphitheater located at the South entrance to the park. About 90 minutes after sundown is will be so dark that:
1. you can't see your hand in front of your face
2. you'll see Russian spy satellites passing over monitoring our missiles
3. If it is a clear night, with no moon, the sky will be full of stars. There will be almost no black in the sky. It will be all stars. You'll be able to see the Milky Way Galaxy.
If you go, take a flashlight. it is really dark. There may also be a range talk during this time.
Hot Springs, SD. This is the home of the Mammoth Site. It is an indoors active archaeological dig. It is an impressive look at the remains of Mammoths.
At I90 exit 9 in Wyoming. Medicine Wheel National Landmark go to Medicine Wheel National Historic Site - Wyoming Articles & Tips - Wyoming Travel and Tourism
and read about it. Park the RV at one of the CGs along I90. Route 14 is not good for RVs. If you go, at the split between route 14 and 14A there is a nice local restaurant to have a meal at. No matter the temp at I90, take warm clothes. The Medicine Wheel is at 10K' elevation ind there could be snow year around.