I'm Lucy, and I'd be happy to answer your questions today. I'm sorry to hear about your situation.
If the father is mentally, verbally, and emotionally abusive, that might give you grounds to seek full custody and only allow him to visit once he is able to show that he's received counseling, which could include anger management or parenting classes (or both). You do have to get the custody order changed before you can leave the state with the child, so you can get permission to move.
The judge's ultimate goal is to determine what is in the best interests of the child. They can be a little more flexible with a three-year-old who isn't in school yet, but you may want to see if you can set the order now to say who gets to enroll the child in school (and where) and discusses what the parenting plan will be at that time, or you'll be back in court in a little over a year. For now, you can really share custody in any way the two of you find feasible. Maybe the child could trade off every month. Or maybe you could arrange it so the child spends half of each month with each of you (that would be a LOT of driving, though). Or if you can convince the judge of the benefits of living in Idaho, maybe it would be possible to agree now that your child would visit for one of the major winter holidays, a month in the summer, and maybe a couple of weeks in the spring/fall. Essentially, when you work out what is feasible, you can try to convince the judge that it's reasonable.
If you have any questions or concerns about my response, please reply WITHOUT RATING. It's important that you are 100% satisfied with my courtesy and professionalism. Otherwise, please rate my service positively so I am paid for the time I spend answering questions. If you are on a mobile device, you may need to scroll to the right. There is no charge for follow-up questions. Thank you.