If your mother owns the house, then no, his only right is as a tenant. As a month to month tenant he can be evicted by the landlord with 30 days notice.
This answer is intended as informational only, and does not constitute legal advice or form an attorney-client relationship between us.
You husband has rights as a lessee. presuming you and he executed a lease with your mother. If you do not have a formal lease, than you and your husband are what is called tenants at sufferance which means you have a month-to-month lease with your Mom she chooses to renew each month. In the absence of a lease, the law will create a legal fiction of a lease (this is so the Court can use this legal fiction lease to enforce terms and conditions). Rent is typically paid once a month and property law has long held that in the absence of a writing to the contrary, leases are considered to renew each month.
If your Mom wants you so-to-be-ex out of the home, she should send him a letter giving him the necessary 30 days notice to vacate the premises. Neither you or she can just kick him out (unless you have violence or threats of violence from him in which case you may wish to consider an order of protection), but after those 30 days is up, your mother can file for eviction against him.
If you and your husband have a written lease, follow the lease guidelines.
This is all about leasing, not ownership. Unless your husband is on the deed to this property, it is not his and no Court, divorce or otherwise will grant him any rights to it. You may wish to consult with a Lake County attorney who specializes in Divorce.
There are some excellent family law practitioners on Avvo or feel free to email me at DavidZipp@lawyer.com and I will give you a referral to my preferred family law practitioners.
Happy New Year and best of luck in your situation.
This answer is marginal legal advice and does not constitute an attorney-client relationship. Every client and case is unique. The best advice is to always consult with an attorney. Free legal resources at www.ZippToCourt.com
Unless there is an order in your divorce case that he must vacate, then your husband has a right to remain there until eviction proceedings result in an order that he leave.