Although the Head of the House of Bagration-Mukhranski claims to be Head of the Royal House of Georgia, there is no historical, customary or legal justification for this claim. Salic laws of succession never applied to any of the Georgian Kingdoms. Indeed the final unification of the kingdoms of Kartli and Kakheti rests on female inheritance. There are numerous descendants in the natural and female lines, of the Houses of Kakheti and Kartli, and of Imereti, possessing superior claims to Regalty.http://www.4dw.net/royalark/Georgia/georgia.htm
NOBILITY:Copyright ©Christopher Buyers
The Georgian nobility was largely organised on a military basis, the army being divided into several corps represented by "banners" (or drosha), each commanded by the great grandees of the realm. These grandees were petty sovereigns within their own domains, enjoying the power of life and death, but owing allegience to the king. During the seventeenth and eighteenth centuries, the order of precedence was as follows:
1) H.M. The Most High King.
2) Princes of the Blood (batonishvili).
3) Great Officers of State:
b) Chief Secretary (Mtsignobarth-Ukhutsesi).
c) Lord High Steward (Mandaturth-Ukhutsesi).
d) Lord High Constable (Amir-Spasalari).
e) Lord High Treasurer (Medchurchleth-Ukhutsesi).
f) Lord Great Chamberlain (Msakhurth-Ukhutsesi).
g) Grand Armourer (Meahjret-Ukhutsesi).
4) Grandees of the first class (Sul-didibuli-tavadi) of the Kingdom of Kartli, commanders of banners (drosha):
a) Prince of Mukhrani (Mukhrani-batoni), head of the house of Bagrationi-Mukhrani. http://www.4dw.net/royalark/Georgia/nobility.htm
You see - princes Bagration -Muhranski were not a Princes of the Blood in Kingdom of Georgia.