The likely problems are electrical noise in the air conditioning equipment grounding conductor, and the compressor motor reducing the power factor. Without knowing whether your subpanel is breaker-fed or subfed through the lugs or the type of feeders (BX, Romex, Greenfield etc), the only suggestion I can make is to swap the 2-pole breaker/circuit to the ac unit with two circuits from the main panel that have no motors or fluorescent lights on them.
As far as a separate line is concerned, this would require a separate service (and meter). Utility companies usually don't allow this for one occupancy unless local building codes permit.
As far as a separate line is concerned, this would require a separate service (and meter). Utility companies usually don't allow this for one occupancy unless local building codes permit.