I have recently obtained a divorce. I currently have custody of our 3 year old daughter. The mother lives in Alabama and has visitation 8 weeks a year (spring break, week after Christmas, and 6 weeks over the summer). I recently obtained a possible job offer in the Salt Lake area of Utah. I was wondering the process I would have to do here to be able to relocate out there.

It depends on what the court order says about legal custody and decision making. You should set up a consultation to meet with an attorney to discuss your options and how you should proceed.