I don't know.
I remember something similar in Journeyman where the main character had travelled back to the night his son was conceived and due to his actions changing the timing of the conception the child was now a daughter. His wife, who knew he traveled in time but was part of the changed timeline, was invested in keeping the daughter she knew, the main character was invested in changing the timeline back to recover his son.
I see John as the mother in this scenario. He has John Jr and Sara isn't real to him. I doubt he would see Barry travelling back and restoring Sara's life aa a solution- but once it was done he also wouldn't be happy to let Barry change it back to restore John Jr as it is now Sara who he knows and John Jr is the abstract idea.