I think you should tell the g/f that you would love to continue the relationship with her but you are still committed to your wife also.
Let her know hat the relationship with her can continue and flourish but ONLY if she is agreeable to meet with your wife. If it continues as it is, all of you will be torn and resentful which will ultimately end the relationship.
Hopefully the g/f will understand and agree to meet your wife. It sounds like she wants you all to herself and not open to sharing which to you is not an option.
Best to get it out in the open and discuss it now.