As someone who has dealt with bad depression, anxiety, and stress, I can tell you that you need to approach this carefully, for her. I wouldn't do anything without talking to her first (if you go straight to your SIL, your MIL could feel like you see her as inadequate or unable to take care of herself). And you want to be careful approaching the issue with her. The fact that she already talks to you about it is a good thing - she probably feels like you're someone that isn't going to judge her for not being able to handle it, and she knows you already know about it. But the first thing I would do is ask her what she really wants to change. She may love watching her grandson but feel tired afterwards, and just want to commiserate. Or she may want a change and only watch him a few days a week. Or maybe she needs more notice, or something. The key to helping here is to understand what she really wants (she may not know, just ask the question and then let her talk it out). Then suggest that she bring it up with your SIL.
I would bring up one issue with your husband and let him mention it to his brother. If your MIL is starting to feel burned out and stressed, and this kind of thing has led to suicidal behavior before, it could be dangerous not only for her but for the nephew. If they (your husband and/or his brother) see any of that pattern emerging, then she needs some sort of help!
Be supportive and loving of both sides of the issue, no matter what. I was on the other side of the coin (except that finances were an issue, most of the time) and when my SIL "intervened" it was really upsetting. She was in a totally different situation, financially and otherwise, and I felt like it wasn't her place to tell our MIL that we should be paying her when we were barely making rent. It's affected how I view the relationship with my SIL even now (years later). So approach the situation delicately, I'm sure you don't know all of the issues involved for your brother-in-law and sister-in-law.