I'd like to change it to the county I live in (where I also have another child support case too).
Criminal Defense Attorney
As the payor you cannot change the site of where the child support case was opened; that county/state has jurisdiction over the matter, especially if the child is residing in that county. The fact that you have another child support case open in the county where you reside is not relevant as to the other case. It simply means that you have two child support cases opened; one in one location and another in another location. You should, however, make sure that both counties/courts are aware that there is another child that you are paying child support for. Your obligation to be paying for one child certainly impacts your support obligation(s) on the other. If they are not aware you need to request support review in both cases.
Child Custody Lawyer
If the other party (or parties) does not object, you should be able to transfer venue to the county where you currently reside. Otherwise, I wouldn't expect the court to grant that motion unless you can show there would be no prejudice to the objecting party. For example, if your case is in Hennepin County but you now live in Wadena County, the Hennepin County court is almost certainly not going to transfer venue over the objection of the other party if the other party still resides in or near Hennepin County, or Hennepin County itself is involved as a party to the support case. But if the county attorney's office is not involved and representing the county itself as a party, and the other parent resides out of state or in the same county you do, then a transfer of venue shouldn't be a problem even over the other party's objection, for the sake of "convenience of the witnesses and the ends of justice." Note that the motion to change venue must be brought in the current county of venue --- not in the county where you'd like to transfer to. Here is a link to the Minnesota Statute governing court-ordered changes of venue in civil cases: https://www.revisor.mn.gov/statutes/?id=542.11