If my mother-in-law is living in a house that I own and is only in my name, how do I go about having her removed from the residence if she is there with my soon to be ex wife? My wife's name isn't on the house paperwork anywhere. I want my mother-in-law gone because she is the source of my wife and I's problems

You go through the eviction process as if she was a regular tenant. Give her written notice to vacate according to local law. If she refuses, then follow it up with going to court for an eviction order.

However, your wife could file for divorce, possibly put ownership of the property in question which could delay the eviction process.

In Alaska, an action for eviction is called a "forceable entry and detainer" action.