Personally I would tell my MIL to stop, I would explain she can hurt the baby by spreading it. I would teach her the basics, and tell her it makes me worry. Maybe she doesn't know?
Weird! I personally get coldsores every now and wont I won't kiss anyone until it's cleared up, including my baby and husband! So it's weird that someone who gets them would kiss the baby. Hopefully she doesn't kiss the baby when she actually has the sore. At that point, "peace" isn't an issue. I've restricted extended family who wants to kiss her to anywhere but hands and face. I kiss my baby's cheeks all day and really don't want to be kissing where other people have. But as an adult, she shouldn't be offended if you ask her not to kiss her when she has a coldsore because it's quite obvious, especially if she's been living with them for a while. But if it were me, I'd probably have my husband tell her because it would be easier coming from him
Sadly you kinda have to keep the peace but I would start looking for a place now and see what you can and try to sit down and talk about boundaries