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From a Georgian perspective this does not matter. Happy or unhappy, the dynastic problem may have been settled even though the bride's father has declared himself head of the royal house she is his elder daughter (albeit with children by her first husband).
But primogeniture is not and never has been the sole or even a necessary criteria in the Georgian royal house. None of the rest of Prince Davit's own branch has show any interest in the claim, and if Anna's father makes it absolutely clear that he considers his new grandson his heir then there can be no grounds for a future dispute.
In the history of this family there have been other similar marriages between members of different lines that have served to insure the continued tenure of the throne by male line Bagrations.