My cats are the same, they are very loving to us but extremely cautious of others. When Jock (RIP Baby) was in the vets recently, because the staff were so friendly and were brushing him and giving out loads of tlc he was letting them take blood without sedation and wasn't bothering much when they gave him tabs or injections. Just shows what a kind voice and that little extra effort can achieve !!

Anyway, sounds as though the new vet was a wise decision and Cubby will receive better treatment, poor wee soul !!