How many of these long trips are you making? Depending on number might be more economical just to rent for that.
I also have 3 kids, a dog, and don't live near a city. If I lived in a city dogless and childless something like Zipcar would make much more sense.
BTW: The "transaction cost" (time) of frequent car rentals is a non-starter. One of the things I hate about renting a car is that every time it's a different car, some I like, some I don't. I just want to pick out a car I like, have it ready when I need it, have it set up the way I like it, and have my "box of crap" in the trunk where I know where it is.
I don't want to navigate through a young ambitious salesperson trying to sell insurance, or the AI car scanner charging me hallucinated wear and tear.
Americans buy the car for the 1% trips. In my case, most of my car trips are short, but most of my milage is from long-range trips.
What's more informative is this post that explains Mexican driving behavior: https://news.ycombinator.com/item?id=48634740