If a couple was going through a divorce, is there any way to get the husband removed from the wife's estate if she died before the divorce was final? 

Unfortunately until the final divorce decree is issued a husband and a wife are legally married.  Consequently, until the legal dissolution of their marriage they are entitled to the same inheritance rights as any other married couple.  Anticipation of divorce is not a divorce; no matter the intent of the parties (and here the intitial papers had not even been filed).  Therefore, the husband will inherit.  The question is how much?

If there was a Will, he inherits according to it terms; if there was no Will, then the wife died "intestate".  This means that the intestacy laws of the state where she resided at the time of her death will control just how the estate is distributed.  Typically, it's 1/3 to the surviving spouse and 2/3 to all children (but this varies state-to-state).

If they held any property as "joint tenants with right of survivorship", such as a marital residence for example, then he will inherit outright by operation of law.  That means that the property does not even have to pass through the estate to be probated.  The same for any other assets on which he was listed as a beneficiary, for example, life insurance or a 401K.

You may at this point want to consult with an attorney in the area.  Perhaps they know of a specific provision under state law covering this type of situation, of which I am unaware.