Ugh, I'm sorry to hear about the paint incident. What a drag (although, strangely, just the other night I was wondering how a Jackson Pollock style paint job would look on an egg).
One thing to think about as you approach painting
, is that in the paint world, you can only go "down" in paint strength. In other words, you can put a "soft" paint over a "hard" paint, but not the reverse.
It sounds like you have a latex paint there (guessing by how easily it seems to be dissolving or coming off), which would probably not make a great base for new paint. One thing you can do to try to figure out what you have (hence what you could overcoat with) would be to try various solvents out to see what dissolves the paint and what doesn't.
Even though you don't want to do a big paint job, experience tells me that you might want to consider just biting the bullet and removing your paint so that you can start fresh. Otherwise it can turn into the labor equivalent of "there's nothing so expensive as trying to save a little money."
On the bright side, once you got to grinding (or sanding or stripping or whatever method you choose) it probably wouldn't take you very long to remove a not-so-good layer of paint. It would take some work, but nothing to be afraid of. I mean, it can be some hard work, but it's nothing that takes great skill. And who knows, it might come off relatively easily.
I've had to train myself over the years to think of painting
as "A bunch of time spent prepping followed by a few minutes of applying paint." In other words, although I always want to get right down to the satisfaction of painting, it's really just the cherry on top of the sundae of preparation.
Okay, now that probably all sounds grim, and I don't mean it to. It just sounds like you're dealing with someone else's quickie paint job, that they might have done with some leftover.... whatever paint, and maybe it would be best just to make it history.
I'm sure glad you were able to get the paint off your main vehicle. And that no-one was hurt on the road.