What is the ruling of Islamic law on a dog remaining inside the house, and what are the resulting implications of impurity and odor that affect the wife's health?

Your husband is mistaken in acquiring a dog without need, and his error is compounded because it causes you harm. Advise him gently and explain to him the ruling of the Sharia, and that he incurs sin by harming you. Seek assistance from helpful means to persuade him to get rid of it, such as mediating through influential family members.