You are not being rude at all. You are asking her to act appropriately, and she isn't. There's nothing rude in that (on your part, anyway).
I echo the thoughts of others that you have inadvertently trained your MIL to keep persisting in order for you to pick up the phone, and given her the message that she can control you through sulking. I'm sure she knows about your preference for her to call outside meal hours; it's just that she doesn't seem to see this as important. And if you've already explained things to her, then a sit-down and a talk might not do much.
I had a similar situation with my own parents--they used to ring me at all hours of the day for no reason at all except things like "I'm at the supermarket, which kind of cheese do you think I should get this week?". They tracked down my work phone number (not too hard to do through Google) which I had carefully not given them, and I started getting messages dozens of times a day from the front office saying that there was an "urgent" or "emergency" phone call--they would always be about something trivial. I found that if I said something like "I can't talk now; I'll call you back," they'd always just see it as an opening and talk more. It never made a difference if I explained things to them. So I'd just say "I can't talk now because I'm busy/eating/working/etc. and I'll call you back later, bye!" and hang up. There wasn't time given for a response, and they learned fairly quickly that ringing me at work got no further response, so they stopped doing it.
It might help to do the same with your MIL--say you can't talk and will call her back, and end the call without letting her start up a conversation. If she gets upset, that's her personal business, not yours, since you haven't done anything wrong. Just don't give her an opening to respond, since she's shown that she isn't going to respond appropriately. As for mental health issues: is she aware of other numbers to call when in crisis? If so, then you needn't feel so obliged, especially since she is clearly taking advantage of you and controlling you with threats of a foul mood.
Or you could get an answering machine and have your phone go straight to it during meal times. Just make sure it isn't one of those ones that plays the message aloud while it's being recorded, or it will be just as disruptive. Whatever you do, be consistent, or you'll simply give her the message that she has to work harder, and that's the last thing you want.