Very unlikely that he could stay on - "freedom of speech" , "presiding over his household in a good manner" etc. Most would resign before they were removed.
In exceptional circumstances which would have to include virtually all these circumstances - brother refuses to resign , weak or "old boys club" body , totally "out of the blue" affair , no scandal , sympathetic CO , wife very repentant - he might just get away with staying on. It would certainly help if the wife was privately reproved & the matter was hushed up.