illegal alien

My husband and I have been married for 11 years, he is undocumented and has been deported two  times and has come back. 

When I first met him he had been deported once, and entered again illegally,We married I paid to get him legal, he had a green card that he let lapse, he was deported again for the second time. He has returned again illegally.

He is also married in Mexico

Now we have a lucrative lawn service and he has cheated on me many times, I have proof I caught him in the bed once and now his girlfriend has called me and he has acknowledged the fact that she is indeed his girlfriend and he has asked her to marry him and have his baby.  He is 50 she is 26 I am 52 go figure.

The question is about my house that has been in my family for years.  My brother was owner of my house and we, were buying the house from him we paid some on the house together, but then my father died and left me enough money to pay my house off and I did just that I paid the house off.

The property consist of a house and two rental trailers.  Since my husband and I took out a home improvement loan of $25,000 which he left before the first payment was made.

He left, he took the business and all of the equipment that we own and he keeps all of the money, he has not paid anything on the loan or the bills for the house or taxes

Now he has left his girlfriend, and he moved into one of the rentals on the property and he is not paying rent which takes money away from me.

My question is with him being illegal in the country, married in Mexico before we marrieed, he cheated run off with a younger woman etc....does he have any claim to my property?