If he refuses to let her marry any person, even if the proposer is decent and faithful, and staying unmarried is posing big difficulties for her, then in this situation she doesn’t need his permission to do a marriage contract.
My recommendation is to pressure her father to agree to her getting married. Let her mobilize many people to talk to him. Doing Mut’ah may cause her difficulties later if her family or community finds out. It could negatively affect her standing and reputation, so from this aspect I would not recommend it.