A "Royal House" is quite distinct from a ruling dynasty in a monarchy. Any "laws" that govern succession in a ruling dynasty in a monarchy are one thing but in a republic, as these laws have been abolished, they no longer exist. There are no rules because there is no monarchy! In real terms, a "royal house" which doesn't reign has no constitutional significance whatsoever unless (as in the case of Montenegro, for example) it is accorded a constitutional status.
Therefore, any of these old rules are only "applied", if at all, by the mutual consent of those concerned. Alternatively, power to make/change rules is vested, again by mutual consent of those affected, in a recognised head of a house. If it's possible for any head of a house to establish rules regarding succession or marriage, it's also perfectly possible for a later head of house to change them. If it's not possible to change anything in theory but a head decides to change them in practice, no laws say s/he's wrong because....there are no laws! It's a jungle, a mess, a free-for-all.
As time has gone on, we've seen various rival claimants emerge in Italy, France, Russia, Saxony and Romania, to name but a few, and so it will continue. In the Middle Ages, they formed factions, raised armies and fought wars to settle these disputes. Today, fortunately, all they (and more often than not, even more so their 'supporters') are arguing over is a name................
and if in spite of all their arguing, their country were to decide to reinstate a monarchy, the choice of monarch would not depend on them anyway, but on the citizens.