If I buy a home with my married daughter in Arizona does her husband have any rights to it if they divorce or if I die

You do not provide enough information to give a specific answer to this question, and the answers may be different for divorce and death. If your daughter contributes part of the cost of the home, or contributes to its upkeep, in either case using funds she earned or acquired during her marriage, there will be a claim on the part of her husband that her interest in the home constitutes community property under Arizona law. If you provide the entire purchase price and merely name your daughter as a co-owner, then her interest in the house will more likely than not be deemed to be property of the marital community. What happens upon your death depends on a number of factors. First, your daughter's interest in the house is always her interest, whether she dies or not. That portion of her ownership of the house may or may not be community property, as discussed in the preceding paragraph. Upon your death, if your daughter inherits your share of the house, too, then the inheritance will likely not be community property, Your mileage may vary. You should consult with an Arizona attorney prior to the home purchase.