I used to work at a u-haul back in 1999-2000ish, and I remember that we had a book to check what each vehicle could safely tow. In order to rent one of the car trailers I believe you needed a sturdy 2" hitch, a v8 and I think a full ton truck. I'd call u-haul and ask what your truck is rated for in their system.
I, believe back then people would call with the v8 explorer/Blazers or the smaller v8 sierra/f150's and we would have to break the bad news: car dolly only, no trailer. I can't remember if the suburbans were capable or not. You had to have a something more like a f-250 or f-350 in order to rent the auto trailer.
I'd say if uhaul will let you rent the trailer and, I stress this, allow you to get insurance on the trailer, do it. I'd really suggest you take the insurance, because the trailers are a toss up. Our store was a busy location so we typically had newer trailer, but the ones that come in off the road were awful. Take that walk around inspection serious.
If your truck isn't listed as being able to tow the auto trailer and mustang, they'll let you know. Just don't lie about weight, because they'll try to screw you if you need to make a claim in case of an accident, ie. if you're over weight or pulling it with a different vehicle then what you told them. Cheers.