This woman does mean a lot yo your husband. And it seems that what you find particularly hurtful and probably humiliating is precisely that he lets the world know that this woman means a lot to him. It is not a clandestine affair for him: no, he takes her to outings with his friends. So he essentially prefers leading a life where he has a wife who is the mother of his children and whom hr spends little time with and a steady mistress whom he does spend quality time with and who socializes with his friends. If you do not like this life situation and have financial means to live independently from him, proceed to taking steps towards divorce in consultation with a reputable family law attorney. If this is not a realistic possibility, accept the reality "as is", do not go into these futile repeated cycles you described in your post. Your husband will not stop seeing that other woman.