Utah considers that if you are irresponsible with alcohol, you will be irresponsible with a firearm. So does every other State that grants Concealed Carry Permits. Get used to it.
The prohibition in Utah is not absolute though. If you have extenuating circumstances or have gotten help for an alcohol problem, and can prove it, you can apply to the Utah BCI for an official "expungement" of the offense relative to Utah law. In any event, if you apply for a Utah permit as a non-resident, and Utah finds out about an alcohol offense (especially DUI, a felony in Utah, or going armed while intoxicated), forget about ever getting a Utah permit.
Having said that, I used to live in WI (moved 18 months ago) and I and many of my friends applied for and got Utah non-resident permits. They are good in 3/5 of the USA. Utah permits held by non-residents are not good in Michigan, Florida, New Hampshire, or Colorado. These States honor the Utah permit, but only if you are a resident.
You can take the training in WI and apply by mail. Utah is a "shall issue" state.
Utah publishes a list of out-of-state instructors authorized to conduct training for the Utah CFP.
CFP - Utah
CFP - Nevada
CFP - Florida
CFP - Pennsylvania - because -
When seconds count, the police are minutes away.