Wa `alaykum As-Salamu wa Rahmatullahi wa Barakatuh

 

I am not sure by saying who is responsible. Everyone is responsible for his or her own deeds at the Day of Judgment.

 

But if you meant, the father prevented her from marrying a good Muslim man who came and asked for her hand and for no legitimate reasons, then yes he is liable for that in front of God.

 

Parents should help bring to their daughters the best candidates that will take care of them and should focus on two main things; ethics and Deen.

 

Almighty Allah knows best.