You would not need to transfer antimatter. You want to send over power and life support, so the worst connection would be EPS plasma. It's not fun and would require a beefy connection, but it would be fully viable. The whole point is the other ship can turn off it's antimatter core and do repairs and maintenance that cannot be done while the reactor is running.I remain unconvinced your dream of a full umbilical is viable. It would only be able to extend so far while maintaining the minimum thickness needed for containment measures while transferring AM and having multi-hundred kiloton starships within at most a few dozen meters of each other while manuevering is sketchy as hell to me.
The antimatter fuel transfer would happen via the cargo container pods, likely tractored around by the workabees and with it's own dedicated connection port.
And you would absolutely not maneuver while connected. You would maintain 0/0 velocity to one another and sit dead in space pretending to be a station docking port. You likely have tractor emitters near the umbilical to keep the ships from even slightly drifting.