Which is more important: warding off temptation from oneself and from Muslim women, or the parents' رضا (pleasure/contentment), in case of a conflict between them?

It is not permissible for a Muslim to enroll in mixed-gender educational institutions, and the fundamental principle is to avoid studying at a mixed institute. However, if there is no institute free from mixing, and you are in need of studying, then there is no harm in continuing, provided you fear Allah, avoid mixing with girls, and associate with righteous people.

As for shaving the hair, if it is highly probable that it will prevent temptation for you and others, then there is no harm in it, even if your mother disapproves, while trying to appease her as much as possible.