There isn't a right or wrong answer to this situation. You need do whatever feels right to you, and be able to live with the consequences (even though you can't predict them).
This lady may simply be one of those kindly, interested, well-meaning women who like to be helpful to others, and it sounds like you (and possibly your mom) are not the sort of personality type who appreciate that. And since your mom has basically invited her into her financial life, as it were, she must feel that you trust her to some degree - and she must trust your mom as well.
When the nosy person is your manager (did I understand that right? This lady is your mom's manager or is she just considered a co-worker?) and you want to keep your job, it can feel uncomfortably risky to tell your manager "none of your beeswax," so your mom's instinct to say nothing may be frustrating but may feel more secure to her.
If the nosy person is the employee, then it can be uncomfortable to confront an employee that you need and depend on. Finding trustworthy, qualified replacements is not easy in every situation, even when jobs are hard to come by and applicants by the hundreds.
Sometimes a nice way to begin the confrontation process is to just thank the person for being a caring person. If their goal is to feel like a caring person, and you satisfy that, they may not feel the need to be so nosy. If it increases the nosiness, a specific thank you for their advice/observation can be given, so they know that the specific advice they gave "got through." Then they might feel like their obligation to get their point across has been satisfied. If it gets worse, a "thank you so much, but ...." answer would be the next gentle response. Whatever is true, like "I know you are concerned that (my daughter is spoiled) but I have found that (giving her freedom, a bigger allowance, whatever) has had a really positive effect on (how she treats other people, how much she helps me at home, how she feels about herself, whatever), and it is working for us right now. But thanks for the heads up. If I notice any problems, I'm glad I have your advice about not spoiling her in my mind."
When you treat people with respect, you are more likely to come to agreements you can both feel good about. And if the woman can't handle that sort of dignified and respectful series of responses, I can see why your mom would want to change jobs!
There is really not much to be gained by telling this woman "It's none of your business" in a confrontational way. It doesn't put her in the mood to cooperate, and it doesn't convey what you want the relationship to be, and the momentary sense of power can melt into shame when you realize that it was a subpar, immature way to deal with the problem.
On the other hand, if none of the subtle, respectful approaches work, and if your mom really wants her behavior to stop, then using a phrase like this - in a quiet respectful tone, and out of earshot of others - may be the only thing that makes sense to her. But I can tell from what the way you wrote your questions that this really isn't your style, nor your mother's style. No need for either of you to be uncomfortable when there are kinder ways to try to deal with the situation, first.
P.S. - maybe your mom should get her own ATM card?