Watch the trailer fenders on the car door. Many car doors do NOT clear the fenders when the car doors are opened. Those first chips on a new paint job are the worst, especially when they happen for dumb reasons.
The left-hand fender on a U-Haul trailer is hinged and can be lowered so the driver's door will clear with ease. Just remove the rubber hold-downs from their catches on that fender and utilize the hinge to push that fender out of the way.
And I've used a U-Haul Auto Transport to take both my '71 Road Runner and my '68 Barracuda to Carlisle. Both cars fit just fine, um, separately of course...