"...She is becoming heavy handed and arguing.." Perhaps a reminder that an employee is there to do the bidding of the employer not the other way around.
"...Several requests have been made for her not to send the letters without further discussion..." A motion to review the employee's delegated powers of correspondence might be needed.
"...asserting her authority..." It is an authority bestowed (and if necessary revoked) by the council.
"...advising she has the right to correspond with anyone..." A delegated responsibility - not a right.
"...She’s telling us we’re trying to run before we can walk, to only get involved with one topic at a time until we’re up to speed..." Sounds like someone needs a reminder of which end of the dog they are.