AMEN!
There are limits, there have to be limits, and this is a point where limits have to be set. Let CP go off in the sunset with his bikini babe, but don't let her represent the nation as a newly minted princess and diplomatically recognized head of state if she goes to international conventions.
Another option would be that she is not a princess, but ends up being a Baroness and then be there only when CP is, no more and no less. No independent agenda, no personal crusades, no going off on jaunts to UN conventions/meetings and no meeting heads of state in her own right.
Either way, there should be a consequence and condition either way. She has no business getting an "HRH" and if, despite Mabel's many accomplishments, Friso had to renounce his place in the succession to marry her, CP should be expected to renounce or lower his rank.