I fully understand yr thought and situation. My younger brother is now facing problem like you. His son is now being taken care by my mother. Both of them yell nearly everyday.
His son also has 濕疹 on his face and body. My mother uses the old method to handle while my younger brother use the "updated" one.
Anyway, just think about that your mother will never hurt yr beloved daughter 'cose she is her beloved grand-daughter as well.
Also, if possible, don't be too worry about what kind of food your bb taken. My son eats so many kind of food since he was 6 months old. Like 义燒飽皮,腸粉,方飽,pears, water melon, sweet potatos,,,,even ice-cream (which he was screaming to try when he found his father was holding a scoop of ice-cream. He took it by myself.)
U are much better 'cose you are just facing yr own mother. For me, I need to face my mother and my mother-in-law. All of them are using old method to take care of baby.
Therefore,............simply take it easy. Then u will find the way to solve.