That's what I figured.
In terms of succession, the daughter comes first, then the younger sister (in the case of that one crazy princess from the book) then aunts/female cousins.
Eclipsa's mom was dead, Eclipsa was in a crystal, and Meteora was just a babby. If there were no other female relatives, Shastican had to make the call, and even if the call went to an uncle or something, they'd probably also find a fake princess better than a half-monster one.
Why do you think the MHC has a beef with monsters though? The Mewmen are understandable, since they've had a long history of conflict with monsters, but why would MHC care about them? Why do they, a bunch of immoral demigods, even care about the Mewmen in the first place?