A club can make its own rules, you don't like them you don't have to join.
If it's a "you must have flown within 21 days" rule then, unless you post the full wording, we can only assume that it means what you say. So flying somewhere else within the 21 days counts. I wouldn't be surprised if the club wanted some evidence of this, eg an invoice or an instructor's signature in your log book ... but you've read and signed the club's flying order book, haven't you, so you know all this already, so why are you asking us?