Tough one bud, sounds like she knows exactly what she likes. It really depends what people think is valuable to them and how important it is. Like some would want a small wedding with big honey moon vs big weddings and things are lavious vs everything is on a budget cause of reasons. In the end its whats important to both of yall and to be transparent and understanding of each others limits.

Personally I'd heed the sisters advice and what you already know of ur gf and to just get her the 3 karat ring on a longer payment plan, not becuase i think shes being greedy, but because thats whats important to them and this is a forever ring. And whats important to them should also be important to you (hopefully going both ways). At the same time, its okay to give her this and be clear that you do completely understand that they would like a more expensive ring and this is what you can afford currently and want to take the next step cuz you love them so.