And that situation sounds like it is worth the peace of mind for you and the family having a membership with AAA. Which is exactly what I said...in certain situations it does make sense, and the peace of mind is worth it.
Serious problems with a vehicle can't usually be fixed at the side of the road. Even some simple issues like running out of gas or a key that gets locked inside can be a real problem. And elderly or disabled RVers might not even be able to change a tire, much less a dual tire. So those services do offer a valuable service to people that need or want the peace of mind.
But these days, with smartphones, you can often get search results tailored to your specific situation right by the side of the road, and make a call or two, and get help on the way, sometimes better, and quicker, that what will be provided on a contract basis thru the roadside assistance plans. Yes, you will pay full price, but if you only need that kind of assistance once every 5 or 10 years, it might make financial sense for someone to do it that way.
We all make decisions based on our particular set of circumstances.