I just started getting into tcg and have been casually playing against my wife. The other night I used the refinement ability and evolved into a Gardevoir with the same ability. Would I have been able to use Gardevoirs ability?
Yes.
Abilities that specify "once per turn" refer to that specific instance of the Ability. This is the case for Refinement: despite their Abilities having the same name, Kirlia and Gardevoir are two separate Pokemon, and thus their Abilities are treated as two separate instances.
Ability - TCG (Bulbapedia)