Whose name was the house in? If it was in both your father's and mother's names then under Utah law the property would be presumed to be held by the two of them in "tenancy by the entirety". This means that upon the death of one spouse the real estate passes outright to the surviving spouse. In your case, your mother would take over as sole owner of the house.
If the house was held in your father's name alone, it would pass pursuant to the terms of your father's will. However, in Utah, a person cannot use a will or a trust to disinherit a spouse. Upon death the surviving spouse is entitled to what is known as an “elective share” of the marital estate. Generally, this means that a surviving spouse receives a minimum of one-third of the deceased's estate.
You should really consult with an attorney in your area. They'll be best to advise how to handle all of this. If money is an issue, try going down to the local probate court; the clerks there can at times be extremely knowledgeable and helpful.
Also, I've provided a link to a site that will give you some general background as to probate procedures in Utah: http://www.utcourts.gov/howto/wills/
Best of luck.