My ex wants to move out of state and take our son with her. What are my child support rights and do I have to pay an increase of living in the state that she lives in or mine? I live in Minnesota and she wants to move to the west coast.

The courts that settled your case for child support in the first place is the one that should always handle any issues because they will hold jurisdiction. Are you in agreement with the move ? And no if she does gat to move then its not your obligation for her poor judgement and increased costs.

You would continue to pay your child support to Minnesota. The agency in turn would send the money to her in the new state. This is assuming that you pay the child support money to the child support agency versus sending it directly to her. If you send it directly to her then your rate would not increase unless she goes back to court in Minnesota and has it changed.

Your support payments are mandated by the courts. For her to get an increase she would have to petition i9n Family court for a modification of the support agreement. This would probably need to be done in Mn courts.

She can go back to court and ask for an increase, but the courts will be the ones to decide, normally the same court where the child custody agreement is at.

In many agreements there are rules that do not allow her to leave the area with the child ( if you were using your visitiation rights) unless you agree or she gets permission from the court.
But you did not say anything about missing your child or stopping her from moving so you will not get to see your child less.