If it’s under warranty, then the manufacture will cover towing to the nearest dealer and if they are outside of the range, to the nearest qualified mechanic. Hard stop, call the warranty company and have them hash it out.

I hope you'll find an easier way to do it, but if it was me in your shoes, I'd probably drive out to them. You driving the U-Haul with them driving your car home sounds like a good idea. It's the safest option to make sure they don't run into even MORE trouble.

My auto insurance covers tows up to 200 miles, so you need to contact them and verify.
The thing is, even if they only cover 50 miles, they will pay the 50, then you only pay the extra, so I would get some quotes. If you have AAA, then like others said, they never check for id... but I understand why you don't want to worry about risking it, so just drive out there and then call AAA and tell them you were driving their car. Then drive them home in your car while AAA tows thiers.

I'm in Europe where many countries have motorists' clubs that can assist in these situations.

Isn't it called AAA in the states?

If you're going to find a shop for them locally, I would check the ASAs website. Shops who spend the time and effort to become members of the ASA are typicality some of the best shops as far as technical knowledge, fair pricing, and honesty.

https://members.asashop.org/find-a-shop

I'd choose the rent a uhaul and an auto trailer and it to the dealership at the beach for $194 . is it a cost? yes. but it's the most efficient one.

you don't have to spend your day driving there and back. they get to spend their vacation where they planned. they don't have their car while on vacation, but the dealership MIGHT have a vehicle they can borrow while theirs is being worked on.

If your parents have time, they could check if their credit card has any sort of roadside assistance perk or travel insurance.

Did you make sure it wasn't something stupid stopping the car from running? Like does it have gas? Is the battery connected properly? Do some basic checks before you waste time and money getting out there.

See if there's a mobile mechanic in that region that can come look at it. The problem is probably something simple they can diagnose right away.

Then if it's not a simple fix, I would have them tow it with a Penske truck but only if they know what they're doing. You can total a car by towing it wrong.

You should confirm the distance with the insurance, you never really know unless you call or dig through the paperwork. If insurance is eligible/on the hook to cover the cost of repair, they may very well opt to cover a 50 mile tow and have the manufacturer be on the hook for repairs

Edit: They might also be able to cover the cost of tow partially, maybe they'll only cover the first 25 miles and you just pay out of pocket for the remainder

Rent a box truck large enough to hold the car, and a wrecker with a flatbed truck on each end to load and unload.

Might be more expensive than the trailer.

Leif's handles towing and dropoff. I'd call them. Not sure what their cost is like.