The house of Zedguinidze-Amilakhvari had formerly served as hereditary Master of the Horse to the Georgian Crown (Amilakhvari) and retained their princely dignity during the Imperial Russian rule of Georgia.
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Dimitri's grandfather, Ivane Amilakhvari (1829–1905), was an eminent general in the Russian army.
Givi, son of Prince Andukapar, was born of the prominent noble family of Amilakhvari, with family links to the ruling house of Bagrationi of Mukhrani.
He was born in the village Chala in what is now Shida Kartli region (then under Russian rule) to a prominent Georgian aristocratic family.
Kashveti was built on the site of a damaged church built of brick at the request of the Amilakhvari family in 1753.
Restored by Prince Givi Amilakhvari in 1733, the monastery was raided and the monks massacred by the Persians less than two years later.
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It saw a relative revival when the Georgian king George VIII (r. 1446-1465) granted Shio-Mgvime and its lands to the noble family of Zevdginidze-Amilakhvari to whom the monastery served as a familial burial ground up to the 1810s.