WTF!!! He's not even in love with her. He just hate the fact that a person who used to like him doesn't even want to associate with him and prefer to spend time with her husband. He's so childish. He can't have her so he's going to destroy her. The duchess was always kind to him out of respect and he's acting as if she betraid him. Also, he need a brain transplant. Do he really think she'll be able to open an illegal commoner's store without her husband knowing? She have Alphonse by her side and no matter how much he may be blind by love he's a model citizen that will always follow the legal procedures.
Even his father tried to stop him because he knew you'll make a fool of yourself but you couldn't see the big picture. You just though he liked the duchess more than him. Im rolling my eyes right now. Even if she did did illegal things, she have a high status. This will not completly bring her down.