I see a thread lock in your near future ... just sayin.
About your L matters though. My guess is the judge will play nice with anyone that can show her an easy answer to these things. Your L not being there to point out this will not go down easy was bad. Be sure to let this potential L understand.
If you do switch, ask how that could play to the judge. What impact would it have for new L to say you were not properly represented, and you have not been given fair consideration for your needs? Make the judge see this is getting uglier, not easier.
Ask the maybe-new L about any past cases creating a precedent in this court ... women that needed to move and were allowed. What JA wants or does not want should not discount your desire to live near your family and the support they will provide. Start a long unreasonable list of the support they could provide and demand JA match it 100%.
A six month trial does not provide the long term safety net you need and the court should get ready to monitor JA until the kids are 18 or until you are finally allowed to move. End of story.
Does the judge want to see you come back every six months asking if you can move yet? !!!! Suggest that moving is your ultimate overiding desire and the only thing in your way is the cost of returning to court often. Suggest that improving your earning ability will only increase the likelihood of your frequent appearances in court.
Good luck on the L tomorrow. As always, you and the kids are in our thoughts and prayers.