Ditto on what Chillman 88 said. Better safe than sorry keep it together VS having a run away truck perhaps hurt someone else.
I now only use chains with tensioners when towing vehicles on my trailer. After having those 3' straps stretch, trailer flex, or the Jeep bounce and the little hooks unhooking. ( Saftey tip - If you use 3' straps with hooks, my advice is zip tie the hook in place, so if tension releases temporarily they do not become unhooked.) Now it is chains only for me!
Glad you had a uneventful tow! Nice of you to help family out!
It is too bad U-Haul and the rental companies scheme against us and are always trying to keep you from towing what you need towed.(Like the government, trying to fix speed limits for the least common denominator at your expense.) They could just rent bigger ones with higher ratings and surge brakes.
Also try your local rental tool yards, often they have regular sized dolly's (Not the U-Haul specials mentioned above.) and large heavy duty steal plate car trailers for rent. They will ask what you are towing? If you say Suburban they may decline to rent it or lie and say their trailer is too short. (Afraid of liability from rookie towers.) But it probably is not to short (Measure it.), or underrated, albeit it may just be long enough for a pickup. But if you say Jeep they will say "How many days you need it". These are not your medium duty Big Tex things, these are the commercial heavy duty trailers. My yard also says you have to have a 3/4 ton rating to rent their trailers, I feel that is reasonable.
Food for thought - All Suburban’s, Tahoe’s, Escalades, and Armada's have a hitch receiver, you cannot order without one! So you may not find a F150 at your local Budget with a hitch receiver (They order without them to prevent towing.), but their Suburban always has one! So whether you are a mountain biker with a bike rack or need a second tow vehicle for that UTV, ATV, motorcycle or snowmobile there is a way to rent a tow vehicle.
Lots of folks in my area on CL and Offer up who will rent you a dolly or trailer. Also ask them what do they do if the trailer fails. (Surge brakes go out, tire blows, smokes a wheel bearing, etc., etc.) If the trailer is used not sure that repair should fall back on you.
Happy towing!