How can I divorce my husband who's been in and out of jail for a couple of years now?

The basis for a dissolution in Arizona is that your marriage is irretrievably broken, with no prospect of reconciliation. Only one of you has to agree with that statement. With respect to the minor children of a relationship the issue is foremost and always the best interest of the child or children. You should consult with an experienced family law attorney to review this matter.

You need to file a complaint for divorce, have him served, and work through the court system to a final decree. If you can get him to agree to the terms of a divorce, you can save time and money by filing an uncontested joint petition for divorce but everything must be done in the proper legal manner and he must sign. If you want to be sure things are done right and your child is protected, go see a lawyer.

Your husband being incarcerated makes little difference in the process of getting a divorce. Your husband and you are clearly separated (to be "legally separated" requires an order of the court, but Utah does not require a legal separation before you can file for divorce, so simply being actually separately physically means you are separated) by the fact that he is in jail and you are not, and members of couples who are separated file for divorce from each other all the time. So, if you know in which jail your husband is incarcerated: 1) you prepare the complaint for divorce, the summons, and a few other documents that you are required to serve on him; 2) Deliver these court documents to a constable or private process server (you can find these people online by doing a Google search for constable services? or "process servers?) with the name and address of the jail where your husband is located. If the process server locate your husband successfully, and serves him with your summons, complaint for divorce, and other required documents, in the divorce process has been started it is no different for you now than if he were not in jail. You mentioned that you have a four-year-old daughter, but I don't see how your husband being in jail with have any impact on custody of her, unless your husband's criminal history revolves around domestic violence, in which case his criminal record would be relevant to the question of child custody.

Either consult with a family law attorney or go to your local family court and find the self help center and they can show you what forms to file.

Hire counsel. File for divorce. Serve the appropriate pleadings on your spouse. Follow the advice of counsel.