Responses

It’s because she needed her father’s approval in order to become a nun, and the jackass won’t give his approval because it would tarnish their reputation. The only way possible for her to become a nun without drawing too much attention to herself is if her sister marry the prince. With the sister marrying the prince, all the father’s attention would be on them and therefore he would not care about what Vio is up to... or something like that.
Why must her sister get with the prince for her to become a nun? I've forgotten. If they need powerful connections, there should be other high-ranking nobles anyway? No need to panic. Improvise, adapt, overcome! Is she super inflexible or what.