If both parents have joint custody can one parent move to another state

Sure but it's going to change your custody. It is an issue that should be addressed in the parenting plan. In the one I have with my ex, whoever moves gives up custody. There would still be visitation rights but the child stays in the original state.

It has to be agreed upon by both parties involved. There are certain statutes that each state has for this situation. You can look it up online by searching Family Law or parenting agreements for the state you live in. Once the decision to move is agreed upon you can modify the parenting plan to meet the new needs.

In order to do that, they would have to establish who will have sole custody before the parent moves. which would determine if the kid will move as well.

Well usally when you have a custody order it stipulates that neither parent can move out of state with the children. A parent can move out of state if they chose but without the children so if that is the case then the parent that is moving would have to file a motion to ask the judge to change the orignal custody order allowing the parent that is moving to get her or his visitations set up for out of state visits. If this happens the parent that has custody would beed to appear in court so that they can make sure that the judge stipulates that the parent that is moving is to pay for the trips to pick up the kids and to pay to bring them bak. Other wise the parent that has custody may end up paying and you don't want that. What ever you do do it though the courts as far as the visitations go for the children.