First of all, it sounds like a tough situation, so congrats for sticking to your boundaries for the long haul. You said yourself they appear to be making progress without too much drama. So that's great. Hopefully that will continue, but at some point, it may not. You may eventually get to a place where you can't out-dance your mother on the food issue and if you stand your ground things may get tough--but that doesn't mean you're wrong, or being rude. Even if you don't leave your daughter in her care there may be times as DD gets older when she will be alone with her grandma for a few minutes, old enough to eat regular food but not old enough to know she should refuse whatever Grandma offers. Or, DD herself may say something intemperate, as children do, that will start the confrontation. I think it's good to consider and prepare for that.
For the time being, if you want to avoid saying something like, "Your food is unsafe," could you phrase it as a "tastes change" comment? Like, "I know I grew up with this, but as I've gotten older/had a baby/cooked for myself, I've discovered that I prefer other things." Or spin it as, you're trying to eat healthier things that you know she won't have in the house, like veggies and light mayo and whole grain bread.
Also, I don't think there's anything wrong with eating/feeding your child a full meal before meeting your mom for lunch (in this situation), even if you were the one who suggested lunch. You don't have to tell her you already ate, just pick at the food a bit and say you aren't hungry, for some strange reason, so while your mom eats, you'll tell her about your day. Always sounding cheerful and positive. (I know it's generally rude to eat before you meet someone for a meal, so I was thinking of ways to negate that. 1--Don't tell them you've eaten; 2--Be entertaining so your lack of eating isn't awkward for everyone else; 3--Don't let the food they've prepared go to waste--tell them you're just not feeling hungry before they plate your meal, offer to wrap up the sandwich for them to have later, etc.)
I also agree that if at all possible, direct the get-togethers away from food. Meet "after lunch" with a firm plan to leave "before dinner," including a mid-afternoon snack from someplace else so dinnertime can reasonably be pushed back until after you leave. If you're trying to avoid eating her food while also avoiding saying that, avoiding meet-ups at mealtimes is the best way to start. Think of it like situations where two people are friends and want to do stuff, but Annie knows Betty doesn't have a lot of spending money--the usual advice is for Annie to 1) suggest activities that don't cost any money; and 2) offer to pay Betty's way when Annie really wants to do something that costs money. But Annie can't always do option 2--she may not be able to afford it, Betty may feel patronized/offended, etc..