My reading of this slightly at variance with that of previous posters. So here goes.
The world of our kids is slightly different to that of our dc. Yes, they overlap and intersect but so much our dc's journey to adulthood is conducted just off and to the side of our world and, significantly, is conducted through their relationships with their peers. Negotiating the points at which we swoop in and offer advice/intervention is really, really tricky.
Your dd's mum is crossing the line. She should butt out and maybe even get a bit of a life. Harsh but true. HIf she really is discussing your dd's and her dd's relationship over coffee with her adult mates ... she's going too far. And the fact that you have come to hear of this tells me that other parents think she's going to far too.
On the plus side, she's making no friends doing this. You can bet your life that the people she's chatting to may be nodding sympathetically but are going home and telling their own kids to tell her dd nothing, to tell her nothing and making sure they, themselves, tell her nothing.
She's breaking the mum's omerta and acting as an "open channel" between her daughter's circle of friends and her own. Yes. of course, we all cross that boundary, but the point is, because that flow of information is so precious, it has rules that are all about not violating its inherent confidentiality. No mum wants that flow to dry up!
So, in short, I think, yes, tell your dd to steer well clear of her friend's mum. She's a blabbermouth. And you do too. Whatever you do, do not yourself be drawn in.
You'll notice I've said nothing about the whole boyfriend thing. that's because it is almost an irrelevance. how kids choose to negotiate the complex terrain of friendship and romance is, really, their business. They'll learn what suits them - and there will be tears, no doubt, on the way.
The point is, you're supposed to be able to eavesdrop, so that you can swoop in if things start going pear-shaped. You're not supposed to get stuck in there, your dd's friend's mum is (undoubtedly for reasons of care and concern for her dd) simply in the wrong place. Worst of all, she's risking your whole network of informants by doing this!!
Obviously, if there is more going on, if it looks as though your dd's friend is becoming a scapegoat, or being bullied or something nasty like that then you intervene.