If the man wants to marry a second wife. Islam allows it and what the woman did is going against her relgion. And no, the man does not need his first wife's permission to marry another woman. He just needs to inform her but in the case of Misyaar marriage, he does not even need to inform his first wife..
Personally speaking, I would not mind being a second wife of a married man bcoz as they say half a loaf is better than no bread at all so half a husband is better than no husband at all.. Spinsterhood is unnatural.