We live in Louisiana and when my mother dies I'll inheritance her house and business. If my spouse and I divorce after her death is he able or entitled to any of my inheritance?

LA is a community property state, but property that you brought into the marriage, inherited, or received by gift while married is considered separate. So as long as your mother makes it clear in her will that the house and business go to you, then you should be able to keep both through a divorce. However, other assets such as the income you make from running this business would most likely be split. Here's a site that describes the implications of community property in LA:
Louisiana Divorce Source: State Divorce Laws: Louisiana (http://www.divorcesource.com/info/divorcelaws/louisiana.shtml)