In most states if the widow is not the mother if the spouses kids, and spouse dies without a will, the estate, including real estate is spilt between surviving spouse and children of a previous marriage.
Texas is an inception of title rule state which means that if your father owned the property before marriage, then it is separate property regardless of whether community funds post marriage were used to pay it off. So assuming separate property, the widow would get a life estate in 1/3, and the children would split the remaining 2/3 equally, subject to the widow's life estate. Children would get it after widow dies. The situation may be complicated if there was a note on the property that started prior to the marriage, but was paid off post marriage from community funds. If that happened, then the widow would technically have an independent claim based on the expenditure of community funds while it was still being paid off. This is definitely one of those questions you need to get clarified by an attorney in person with all of the facts and documents in front of them. What I've mentioned here is just an overview of general concepts, and is certainly not good enough advice to proceed with any certainty.
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It is not clear from your facts whether the house is separate or community property or whether or not the widow is the mother of the two adult children. Those facts are crucial in determining the heirs identity. But, there is another issue here. Even if we had all the facts, simply knowing them would not transfer title to the house (and other assets) to the heirs. That requires some type of probate procedure. Because the decedent died without a will (intestate), none of the options are as good as if there had been a valid will. The answer to your question and to the questions you have not asked can only be obtained after consultation with an experienced probate attorney in the county where your mother lived at the time of death.
DISCLAIMER: This is not specific legal advice and does not establish an attorney/client relationship.
My colleague provided an excellent answer. I just want to highlight the fact that the surviving spouse has the right to remain in the home for life.