In fairness to the OP, I suspect that if you aren't the sort of person who prefers to keep family things private, and doesn't want to be discussing them with all and sundry, it is going to be hard to put yourself in the OP's shoes - and the opposite applies too. If you are naturally reticent about personal/family things, then someone who happily shares all sorts of information with lots of people, is going to baffle you completely!
I tell everyone everything, pretty much - if I was Maple's MIL, I would have chatted to people I met on the school run about why I was taking the children to school - that is what comes naturally to me. But if my DIL had specifically asked me not to gossip about a particular thing, then I wouldn't.
The problem has arisen here because Maple is a very private person, and her MIL is the exact opposite. Neither of them are wrong, or bad for being the way they are - but it has caused some problems.
I think Maple needs to have a calm chat with her MIL, to explain that she is very private about family things, and finds it upsetting when things she considers private are spread about. She should make it clear that she knows her MIL isn't doing it on purpose to offend or upset her, but she would prefer it if her MIL didn't talk about her (Maple's) private or family stuff with other people. I would hope that, if she does this, her MIL will a)be sorry that she has upset her DIL, and will apologise, and b)will not gossip about Maple's family stuff in the future.
If she carries on, then she is firmly in the wrong, and Maple would have every right to be cross with her - but I do think she needs to tell her what the problem is - it isn't fair to expect her MIL to guess that Maple is upset, and why.