Ok, I usually do not agree with popa, but he/she is 100% correct. This older lady was in the young girls seat without permission. The girl had her coat on the chair so for all intents and purposes the girl has baylos on the chair while there in shul.
Having good midos does not mean to allow someone to step all over you. If the older women had no seat and the mother saw that, she should offer her daughter’s seat to the older woman. That is showing good midos. However, in this case, there were extra seats and this older woman decided to occupy an already occupied seat. That is bad middos and it is the responsibility of the mother to educate her daughter that people will not tolerate bad middos. There is no chiyuv to be a chosid shotah.