You would need to file a petition for co-guardianship with the First District Court in Brigham City. You would want to be a co-guardian with your fiance/husband. Your petition will want to address how this is beneficial for the children and that your petition does not affect the rights of your fiance. This is something I do quite frequently and it is not really difficult, assuming that there are no objections. That is the one concern here. The mother has passed away, but will grandparents possibly object to your petition?
I know you want an answer, but I can't give you an answer until I have more information. Why do you want guardianship? The children are your fiancee's children so he is the legal custodial parents (I assume so, anyway.) If their mother isn't living I suppose you and your fiancee could Petition the First District Court in Brigham City (btw, I grew up in Tremonton and attended BRHS) to grant you partial guardianship, but the Court might hesitate doing that until you and your fiancee are married.