It is my daughter's family that needs to be ambitious for her to climb the social ladder, stand up for our lives, and leave a good name in history.
It means "ambition". 凌雲 = ascend the clouds, i.e. lofty and 志 = ambition, aspirations, will. So "lofty ambition".
So it's like, "Women need to be ambitious, climb the social ladder, stand up for themselves and leave a good name in history books"