You have a right to feel betrayed and hurt.

I think your wife has done something behind your back. She exchanged pics and developed feelings, then decided to tell you and ask you if she could make out with this woman.

How would you feel if this were a male that she claimed to have feelings for? Exchanging pics and texting, and now wanted to reach out to again?

Sounds like your marriage may have some trouble already if you don't feel loved. I don't think it would be controlling HER, I think saying "no" would be in an effort to save your marriage. And it seems like it's in trouble.

The problem here is that she's already kind of strayed and betrayed you. So either you allow this and allow her to have feelings for this woman, or you don't and you tell her that you want it to just be the two of you, if that's what you want. Seems she prefers something more open though? An open marriage of sorts? Is that what you want?