Where in the play is there evidence to support the argument that Capulet is selfish and cares more about his image than his daughter's happiness?Also, can this argument work?
For sure you can make this argument. Just look at the part in the play after Juliet is married (secretly) and Tybalt is dead. (Act III, Scene 5). At that point, Capulet demands that his daughter should marry Paris.
When she objects, he really just goes off on her in a big way. He says all sorts of horrible things to her and basically tells her that she is going to marry Paris or else.
So there he is showing that he does not really care about his daughter's happiness -- he just wants her to do what is best for him.