[...]Also she wrote me that her daughter hated the headgear and also was a shame of it..
The mother headgaer or her headgear. ( seems the daughter wear one too )
The daughter hated her headgear ?
Your statement could also have been read in a way, that the daughter was embarrassed by / ashamed of her mother wearing headgear.
Most teenagers are - after all - embarrassed by her parents. Especially when the parents do something that makes them stick out of a crowd,
And let's face it: Wearing Headgear is quite embarrassing. Even more when done in public, as the mother repeatedly did.
I personally(!) think that both variants are true: She certainly was embarrassed, having to wear headgear herself. But I also do not find it hard to believe that the daughter is glad that her mother is no longer walking around town with a conspicuous silver contraption strapped to her head.