Roads within Yellowstone okay for towing travel trailer

Stay out of Glacier with the trailer, which shouldn't be a problem, since there is at least one lovely campground very close by. Use the shuttle bus in Glacier.

Yellowstone and Grand Teton, on the other hand, shouldn't be a problem, as long as you leave the trailer in the campground. The main roads are great, side roads, as mentioned, not so much.

You are going to love all three parks. They are beautiful. So much to see, be sure to take your time, and I hope you have the time to explore them thoroughly.