Your council can take absolutely no "disciplinary" action what so ever in relation to a Cllr. The council has no such power.
If the residents association is an entirely separate entity from the town council it should follow its own constitutional process in relation to expelling members.
If the presentations you have done have been on behalf of the residents association so be it.
Neither you nor your vice chair should be 'representing' the view of the council unless it has formally been recorded and delegated that you may. Of course each of you may enthusiastically express your personal opinion.
For exactly the opposite reason you seem keen to impose "discipline" upon your vice chair via the council for representing a view which [you say] is not that formally of the council, you are being hypocritical by expecting your council to discipline the vice chair where there is no mention of the council formally endorsing your personal aspirations.
From what you have written, it reads like neither of you have the mandate of the council...