Princes are responsible for finding a partner to rule with.
Inheriting the right to rule is not a simple process in Adeira. Because each king needs to be able to cooperate with the other king, and must reach what amounts to consensus agreements with the other king, simply choosing the first heir from both ruling families could easily result in ruler disputes that could tear the kingdom apart.
Instead, the princes, princesses, and other eligible potential rulers must find a partner to rule with if they want to take the joint throne. A partnership must have one individual from each ruling family to be considered. The partnership, together, will then present to the ruling kings their case as to why they should be considered to take the throne, after which the ruling kings must come to an agreement as to which partnerships they think would make good rulers. Only if both kings agree to a partnership can that partnership be considered a successor to the throne.
Successors are then granted a duchy to jointly rule, which they must do effectively to remain a potential heir. All potential heirs must be sorted by the sitting kings, although the kings can choose the manner in which such sorting is conducted. First among these is the crown partnership, which serve as dukes of the capitol until such a time as the ruling kings leave the throne, at which point they will appoint a new crown partnership and take the throne.
A partnership is only allowed to rule so long as both partners agree to it.
Naturally, a partnership which cannot abide itself cannot effectively rule. A partnership is dissolved should either partner become disillusioned with the quality of their running mate or die. Partners cannot be swapped out in a partnership, so if one (or both) of the partners wish to remain a potential candidate, they must find a new partner and go through the vetting process again.
This is true even for kings. The quality of one king is no indicator of his skill at navigating any potential future partnership, so if a king dies or otherwise decides to abdicate the throne, his partner also loses their place and the partnership is replaced by the crown partnership. A former king can, of course, find a new partner and be vetted for a dukedom. A former king can even potentially becoming part of a new ruling partnership in the future, and in the case of a king who was formerly a beloved ruler, there may be considerable pressure on the new monarchs to step down and allow the new partnership to rule, but this is by no means required. The new partnership has ever right under law to remain in control of Adeira until such a time as their partnership comes to an end.
The kings rule by consensus only.
The kings wield absolute power over the land, but only if they both agree to it. This belief has been enshrined in both the political sphere as well as in the spiritual one. Humans are seen as quarrelsome by nature, so if two kings can agree on a policy, this is seen as a clear sign that the policy is not an act of man bu an inspiration from above.
While the kings may, among themselves, decide to delegate responsibility to one another, perhaps with one king handling domestic affairs and one foreign, all of their decrees are theoretically made by consensus. Should either king oppose a decision, that decision is not made. Throne room argument and bargaining are common, with both kings often seeking favor for their house and relatives, but this requirement for consensus means that the kings will always present a common front on any decision they choose to turn into policy.
The only exception to this, of course, is in abdication. Any king can choose to remove himself from the throne at any time, dissolving his partnership and removing his former partner from the throne, as well. Of course, this means a considerable loss of personal power, so kings rarely choose to abdicate, sometimes going for years without speaking to one another due to bitterness from internal conflict, while still technically ruling as a member of a joint partnership.