As far as I can tell, the crown (the entity, rather than the object) is really just a fancy name for the royal will. On that will is ownership of the kingdom itself. Which means, in theory, the crown can go to whomever the current holder wants.
The only caveat here is that property rights have to be backed up with threat of violence. If there isn't anyone around to back up your claim then you don't own the thing, no matter who you are or what it is. So it is only through the allegiance of the nobility who hold the reins of the military that the king is able to own the kingdom.
Rules of Succession are kind of a promise by the King that the crown will be passed down following a certain pattern. Your rules of succession may be different than modern England's. There is no "one" way of doing it. But if the recipient of the crown is unpopular enough with the nobility, whether the rules of succession are being followed may be a moot point... Because it's the nobles with their capacity for violence that backs up claims to ownership, not the crown. If there is a disagreement between the nobles who should rule, then you end up with something like the War of the Roses.
But I am not an expert so take this with a grain of salt.