What your mom said was not helpful and maybe next time you could say just that. I have used that with my FIL who doesn't really know how to relate to people at all. I just say that is not helpful and he stops. I hear comments people have made in my head alot and have been trying to just shake off that negative energy. Sometimes I get mad and snark right back but for the most part I just let it go. They are ignorant and don't deserve my energy.
I am sorry your little one got burned but it doesn't sound too bad. Sorry she can't use sunscreen but maybe sun safe clothes would help, even a coverup would probably be enough. I have swimsuits from sunclothingetc dot com that also carries clothes. The suits are cute and they totally work! I also got some stuff from solartex dot com.