Thanks for being so open about things and I am sorry you are in such a tough spot. If you ask that she stop communicating then you are seen and felt as controlling, but if you don't you may not feel much trust. Her history suggests that being unfaithful is part of how she negotiates herself in a relationship so like you, I worry that this will take place again. But even if she stops communicating with these past flings, there i no guarantee that this behavior of hers ends either. So, what to do? I would let her know your feelings of discomfort again and let her know that you will not demand that she end these relationships but for her to think and feel with empathy how it must be for you. She can either keep these going for her own needs or she can mature a bit and see what works for her and her current love because that is where the focus should be.
And if she chooses to remain in contact then so be it and then you will need to see how you feel moving forward and if this can truly work for you and if you can feel trust and safety with her.
I would keep the lines of communication open around this and see if she can't, on her own, come to the realization that what she has now with you is what is important and not hanging on to old lovers. I am with you on this.
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