Q: What happens when there is more than one person attempting to be in control of the meeting?
A: This can be a problem, particularly if there are no agreed ground rules for the meeting.
The chair is nominally the person who should run the meeting. If the chair seems unwilling and/or unable to control the meeting when a third party tries to take control, it is the responsibility of the other attendees to support the chair and regain a sense of order. If this is not successful (and depending on the rules of the organisation), it might be appropriate to adjourn the meeting and reconvene when there is a consensus on how to proceed.