Take care to be sure your trailer and load don't exceed your hitch capacity and other limits of your motorhome. It would not be a bad idea to have a reputable truck shop check out the hitch and mounts and so forth before you set out, as things may have deteriorated over the course of forty years. The U-Haul trailers pull decently, but are not lightweight.
You can avoid the mountains (at least the worst of them) by going west before heading north. Taking e.g. I-65 to I-69 should be rather flatter than I-77. If you look at a topographical map of the US, you'll see that there's a bunch of mountains in the east, a bunch in the west, and a more or less flat space in between them. The idea is to get to this flat space by going around the southern end of the eastern mountains.
The biggest key to driving a trailer down the road is to take it easy, bearing in mind that your stopping distance (and acceleration and most everything else) is worse than without the trailer. This means going more slowly, leaving bigger gaps around you, and so forth. There's nothing wrong with puttering along in the righthand lane of the Interstate not nearly as fast as the rest of the traffic; they build them with passing lanes precisely so the traffic can get around slower vehicles, after all.
