Very good questions. There is a missing point. It is absurd to allow her the title princess. In part for the reasons outlined above. There is a very American tradition whereby descendents of penniless immigrants develop elaborate family trees complete with heraldry as though they were nobility. You have to understand that the "monarchy" here was part of state formation here which a adopted older forms as congenial to circumstance here, a hierarchichical order, without central state power. A monarchy was established for a centralized state here that codified the privilages of the Ali'i, and established private property in land for them. The number of Ali'i were very small, 1 percent, who got 99 percent of the land. And it wasn't a democracy with a king, something like the British. It was an older style, monarchy more like Saudi Arabia, with fewer "princes". She inhereted wealth, in the form of real estate. The underlying question is Abigail not as a princess, but as an heiress.