I have always regarded jealousy as fear and insecurity. A jealous person is concerned for her own welfare and happiness. To lay down so many rules and restrictions in a situation like this is a path that leads to a blow up or break up or even disaster.
By holding tightly to something, you will drive it away. You will lose it. If this situation progresses in the same direction that is likely to be the outcome. There must be a change.
If you raise a bird, keeping it in a cage, then open the cage door to let it chose freedom it is because you truly love that bird and want the best for it. You want it to be happy and free. If that bird comes back to you and lights on your shoulder, you have a friend forever. If it does not come back, you should be happy that you gave it the freedom it desired.