1. Your husband may challenge your ownership to the house on the ground that the consideration of the house was paid by him and not you, and consequently he should be declared as the owner of the house.
2. Even if your husband gets the papers of the property he cannot transfer it to this woman as he is not the owner of the property. Before a person can transfer a property he has to possess the legal authority to make transfer, which your husband lacks. Property papers have scrap value for your husband as he lacks the inherent authority to transfer.
3. The property is registered in your name, so your children and husband will, unless you make a will, get an equal share therein after your life time.
4. Your children have a share in the ancestral property, if any, of their father. They may cull out their share by moving to court.