Welcome to our forum.
You have a tough time to go through, and this other woman may have a tough time to go through as well. Maybe someday in the future your wife will be more willing to negotiate things?
Jealousy is not a predictable emotion. One can have it all figured out, and yet it crops up anyway. Likewise one can find that on one day, the jealousy is unbearable, but then on another day, it can be managed.
It is often useful to talk about the jealousy, in terms of trying to get to the root of the problem. What is causing your wife to fear losing your love? Perhaps there is something between just the two of you that needs worked on. You mentioned that your wife is super busy with work right now, and that you and she aren't spending as much time together as you and/or she would like. Is that something that can be discussed or negotiated?
Whatever you want to talk about, I (along with many others) am willing. Remember, mono/poly relationships can and often do work.
Love means never having to say, "Put down that meat cleaver!"