This is a friendship she had before she met you and it has nothing to do with you unless they're shagging or lying to you, neither of which has happened.
That's not true actually. Many emotional affairs are played out right in front of the partner's eyes purely because it is so hard to argue against an innocent friendship.
But there can be emotional intimacy, thinking about each other a lot, turning to that person to discuss your problems, fears, hopes, worries, etc. All the sorts of things you would normally share with a partner. There can be an emotional connection, an attachment that makes the bond so strong that it can interfere with the primary relationship.
Sometimes people even take their children along to their meet ups, as often it's a good excuse to get together and it all looks totally above board. Eventually, of course, this will often lead to a physical affair, especially if the marriage partner is relegated to the sidelines in favour of continuing the emotional affair.
We can't tell you OP what it is. We don't know because we are not one of the three people involved. But I would say to go with your gut feeling. If she doesn't respect you enough to listen to how you feel and reassure you, by her actions that your relationship really is the one she wants, then you may have more problems to deal with yet.
Hopefully she will rein it in a bit now she knows it bothers you. One thing she could do is agree to not accept any more expensive gifts, for example and not to use flirty language when she communicates with him. That would be easy to do.
However, now that you have expressed concerns she should cool it off with him to show him that you are more important to her. I would ask her to do that and see what she says.