If my mother-in-law passed, who gets her estate?

When there is no will, her estate (the property, including the house, she left behind) passes by "intestate succession," or the rules for who gets what when there is no will. In your state (every state has its own rules, though they tend to be similar), when there is a surviving spouse and children the deceased had with someone other than that spouse: the surviving spouse gets 1/2 her estate and the children from another person share the other 1/2. (This is slight oversimplification, since AZ is a community property state: more accurately, the spouse keeps his 1/2 of community property and gets 1/2 of her separate property, while the children share in her 1/2 of community property and 1/2 her separate property.)
The child of the deceased and the surviving spouse inherits nothing.
Certain property passes outside of probate, like a house owned as joint tenants with right of survivorship with another person: it does directly to the surviving owner or joint tenant. However, you describe a house that predates the marriage, so it was presumably owned solely by her (and would be separate property). In that case, the spouse has a 1/2 interest in the house and the 6 children from a prior marriage share a 1/2 interest (each has 1/12th). If the people who inherit the house cannot decide what to do with the home, one or more of them could bring a legal action (lawsuit), commonly called an action "for ejectment" (your state may have a different name for it) to get a court order requiring that the house be sold and the proceeds distributed among the owners. Any of the heirs who wants to explore this option should consult with a real estate attorney.