This would be my ruling:
The fiendish, vampiric ancient blue dragon named Sharzzakhar, consort to the Great Mother of All Dragons can be gated, and has no choice in the matter, while the Great Mother of All Dragons, who is no goddess but truely is the First Dragon, can choose to stay or go upon being gated. But since while he sits upon the Hoard of the Great Mother, Sharzzakhar enjoys the protection of her Skein of Many Wards which, among other things, protects those within range from being gated.