How do I get her to work for it?

I have a potentially explosive situation: 

Really sexy, fit blonde girl. Responds well to dominant (caveman) type behaviour. My girlfriend, who is generally fine with me seeing other girls, does not like this girl. I am not about to dis my girl to run around with another girl she doesn't get along with, though I think my girl might possibly come around and reconsider if she gave this girl another chance. I think blondie is a bit socially awkward so she sometimes comes across as bitchy.

At first blondie adopted a bit of a competitive frame with my girl. Obviously that doesn't work for me so I infected her with the idea that there's no need to get competitive and there's no reason why everyone can't get along. I've been texting with blondie a bit and she seems to be getting invested.

In order to make this work, I'd like to see blondie seeking to make a better impression mith my girl. This could be really interesting. I think these are both potentially very passionate, even volatile girls and I get the sense that they could either get really along or not in a really explosive, fiery kind of way.

realizing that this is a really unique and bizarre situation and I might just have to accept that I'm on my own here; any thoughts on how to frame, arrange a meetup that sets things up for success? Any thoughts on how to motivate blondie to seek a better rapport with my girl?

im not necessarily just pushing for the threesome here (not opposed to it either). The meetup could potentially be sexual or more casual