There does seem to be a bit of a misconception about the Commonwealth. Obviously it grew out of empire and the Queen is Head of the Commonwealth. But that is a symbolic position only, and is not hereditary. Charles will be Head because the Queen let it be known that she wanted that, but William has said he thinks after that, it probably won't be him.
The Secretary General of the Commonwealth, the person who does all the work, is Baroness Scotland.
Member countries of the Commonwealth include European countries such as Malta and Cyprus, and other countries that have nothing to do with the Queen, such as India or Rwanda (how topical...) Nothing to do with royalty turning up to wave from the back of a land rover.
climate.thecommonwealth.org/
Good luck finding information there about how important the monarchy is. 