D.B.
I think the problem here is undoing what's already been done or allowed. I get how things have evolved to this point and there was no clear moment when things went over the line. And I see that she's a professional relationship, previously a social one (through volunteering) who is also fairly intimately involved with your kids as a tutor.
I think you have to take baby steps unless you want an outright confrontation, which isn't going to work in your office setting. So start with the CPS business - stop discussing whether you agree with her or not. Just murmur, "Do what you think is right" and say no more. If she goes into it more, repeat the same phrase while you are busy doing your work. If she persists, say, "I'm sorry but I really need to get my work done." Don't participate in the gossip, even if you are disagreeing with her assessment - it's still gossip. So you can't change her, only yourself. If pressed over time, you can say, "You know, I'm not too proud of myself for engaging in gossip about others. I really need to stop." Otherwise you can just murmur "Um-hmmmm..." and keep pushing papers or, better yet, pick up the phone to make a work call. But that also means NO MORE SHARING of anything personal at all in the office - no "how was your weekend?" and no "you won't believe what my kid did yesterday." NONE OF IT. cold turkey.
Kids without coats or shoes? Say "if he's cold, he'll learn to take a jacket the next time. Thanks for your concern but I've got this." Shoes? "I've got this." Don't explain that one brand held up and the other didn't. Just "I've got this." You can make a half-joke like "I'm paying you to work on math, not fashion." Or you can stop having her tutor him because the focus is on other things and not his schoolwork. Find another tutor.
If she shares info that others shared with her in confidence, stop her in her tracks. "That info was given to you in confidence, and I don't want to hear one more word." Of course, the next logical thing to say is that you won't share anything with her because she shares with others! She doesn't honor commitments or confidentiality. You can say that outright, or you can say, "You know, Matilda, your concern for others leads you to discuss private matters with other people. So I'm not comfortable sharing things that will go beyond this conversation. Let's just get to work, shall we?" If she's your boss, you have to be careful. If she's not, you'd best understand right now that management will notice she's gossiping about people in the office or even the managers themselves, and you will be considered a part of it. Tell her your job is important to you and you think conversations should be 100% professional and not social, lest you get called in to HR, the boss' office, or even lose your job. (Let her extrapolate that her job could be in jeopardy.)