Considering Peter’s response, your by-laws probably also have the “permission must not be unreasonably refused” qualifier.
If so, failure to respond to a written request and any subsequent refusal on any other grounds than the dog had proved to be a nuisance would probably fall over on that count alone.
Send the EC a registered letter telling them that you intend to move the dog previously described in letters to them, into the unit. That way they can’t say they didn’t know. Then just do it.