In my opinion, your case could go either way depending on the judge or the daily winds. Sometimes, a parent with more residency would be allowed to take the child and move out of state. While you state the move might just be long enough to attend college, most know once the child moves, the chances are good he/she will not return. Other times, the judge may hold great value in the relationship with the other parent and the friendships gained. You've not mentioned if this is a boy or girl. That might make a difference to some judges.
Personally, I don't think a year on/off plan is even remotely a responsible plan. But I also don't think moving the child away from their father is a great plan either. I think parents who've come into difficult times need to sometimes stick it out for the kids. I don't mean stay married, but for goodness sake, try to keep the child involved with both parents.
I kind of feel like there are several details not mentioned here, so it's hard to give much pointed feedback. But, my answer would still be the same - it depends on the judge. And also - dig deep and think about your grandchild and his/her relationship with both parents. This can really be a change of course for a child.