Infidelity Support Group
Any relationship in which one partner engages willfully in sexual relations with another outside of the partnership is considered to have experienced infidelity. This breach of trust is often traumatizing for the faithful partner as well as the relationship, and support is often needed to heal emotionally and to decide whether or not the relationship should continue after...
Someone with severe narcissism and possibly sociopathy simply will not hesitate to use people as objects and weapons in order to get what they want.
Your husband has over and over shown you that he is capable and willing to do this regardless of how this will damage you or your children...his own children.
Stay in the house, get a lawyer, and get this dealt with so that you and your children will no longer have to live in this environment.
More likely than not you would be able to get half of the house and assets, half/full physical custody, and some level of child support and alimony.
Family law unfairly favors the female, but no one is going to cry for your husband...