I think we should respect the OP's gut reaction because it is within a range of normalcy for that situation. Just as not being worried about it is also normal.
Has anyone ever heard of one woman attacking another at the playground, killing/injuring her and/or her children? Perhaps I lead an extremely sheltered life, but I've been on playgrounds almost daily for the last 8 years, talking to lord knows how many women, and I've never heard of such a thing.
Fearing another woman at the playground - and not even at the playground, but at a remove, in a car! - is simply not in the range of normalcy. Trust one's instincts, yes. But trust them regarding what might be a dicey situation. Which this was not, in my opinion.
As to "profiling," if one is going to think that way, one might as well stay in the house all day. I suppose anyone encountered in daily life could be considered a potential "profiler." But that's certainly not the way I view the world.
I don't mean to be dismissive of the OP; she did ask if we thought she overreacted. I think she did.