So as you know, the royal family isn't just restricted to Inkopolis. Each different district, city, or county has a recognized monarch as the main land.
Some things to note about the Monarchy in general:
The monarch's powers are limited by a constitution.
The monarch is obviously either a King (male) or a Queen (female)
In districts/counties/cities where there is no president or prime minister for whatever reason, the monarch takes on these duties. However, in places like Inkopolis the monarch and the prime minister or president are given their own sets of roles or duties. So in districts/counties/cities like Inkopolis, the political system is like a semi-parliamentary or semi-presidential system except instead of having a prime minister and president, they have one prime minister and a monarch (or there may be a president instead of a prime minister).
The consort does not have the same duties as the recognized monarch and has the same rights as a commoner. That being said, consorts can be special in their own ways. Some are firefighters, others are police officers, some even take commanding positions in the military. Consorts can also be candidates for the next prime minister or president unless the constitution states otherwise.
The consort of the monarch is generally either recognized as a Queen (female), or a Prince (male). A reigning Queen can title her husband King Consort but this is generally only done if a reigning Queen marries a reigning King and co-governance or coregency is not allowed in the place where she reigns, but their marriage is still recognized. More information on coregency can be found
here.
Generally, the eldest child inherits the throne unless he or she becomes permanently incapacitated, is given a life sentence with no parole, disappears, leaves, or dies. If he or she commits a crime and becomes incarcerated, either one or both of his or her parents or one or more of his or her siblings will serve as regent until he or she has completed their sentence and is able to be reintegrated into the community again. That being said, once the Crown Princess or Crown Prince becomes King or Queen, they can voluntarily abdicate and the next oldest child will become the monarch.
Some history about -these- monarchs...
In the early history of the monarchy, Inkling society was tribal and the monarchs did not reign over territory but rather over the members of their own tribes. The mate of the heir was generally not one of the Crown Prince or Princess' siblings, but rather an average male or female that was not a part of the Royal family.
However, a natural disaster caused a bottleneck effect within some tribes, leading to inbreeding that later resulted in birth and genetic defects, some of which were so severe they almost wiped out whole tribes so the remaining Inklings of those tribes decided to disband the tribes and decided to sign agreements as to who would own which land so they could figure out who would reign over which land and there, the advancement of Inkling civilization began. That being said, those tribes that were not affected by the natural disaster are not severely inbred and still remain, as I might reveal someday.
In ancient times when Inkling society was still primarily tribal, males and females had equal rights to the throne and both the King and Queen had equal say in decisions that would be made for the tribe, so the spouse was not a "Consort" but possessed the same power as the monarch who inherited their right to reign. However, an imbalance in the gender ratio was what changed the dynamics of inheritance within the Inkling monarchy.
When Inkling society first became less tribal and more advanced, the founding Inklings ended up having more female firstborns than male firstborns, and thus, there came a strong preference for females to reign as previously, the eldest had the right to the throne and crown. Male consorts were also often referred to as King Consorts and females were referred to as Princess Consorts.
That being said, a male could take the throne if he had no sisters after the death of his parents and the reverse was true as gender roles changed.
However, Inkling society became increasingly patrilineal because of another time period when there happened to be a greater proportion of firstborn males to firstborn females that were born within Royal families. Thus, the new Kings began changing the laws and customs so the monarchy could continue without the added inconvenience of having to keep trying again for a female heir and producing more mouths to feed.
Today, Inkling Royal families are neither patrilineal or matrilineal with maybe a few existing tribes that still practice matrilineal inheritance or patrilineal heritage. Instead, the modern, more civilized monarchy adopts practices both from the tribal and civilized monarchies.
And some extras about the Royal Families:
Not all Queens who are married to Kings are Queen Consorts. If a Crown Princess of District A marries a Crown Prince of District B, for instance and both of them recieve the right to reign in their respective areas, they will also recieve the right to reign in their spouse's territory. Keiichi (Crown Prince, later King of Inkopolis) and Azuki (Crown Princess, later Queen of Kelp, where Kelp Dome is located) and the Queen of Flounder District and the King of Moray County are such examples.
That being said, there are issues that can arise although they can be resolved the same way issues in marriage between commoners can be resolved.
However, there is one issue that is most difficult to resolve between co-monarchs and that is who to name as heir of who. This is explained in detail in
this post.
Commoners ARE allowed to marry into the Royal Family as long as they are Inklings. All other races/species are prohibited from marrying into the Inkling Royal Families. However, they are only recognized as Consorts.