wherein rhaegar wins the war, and jaime manages to keep his head by taking a stark for a wife; or five times jaime lannister braved his marriage and the one time he was brave for its sake

When Dorne became one of the Seven Kingdoms, they agreed to replace the Westeros Law of Inheritance with the Dornish Law, so that the same laws would be followed throughout the realm. Or, Five times there was no male primogeniture in Westeros, and this wasn't as helpful as you might expect.

The king is dead, but a cousin cannot inherit before a brother, or before a sister.