kunilou, she had the right to insist anything she wanted to. You, however, had the right to say no to her.
Would you have been cheating if you had continued the friendships? In my mind, no, as long as you told her about it, but I’m not so sure she would agree.
I agree with the general trend of things here - if you wouldn’t do it with your SO in the room, then you shouldn’t be doing it when they are not in the room. If you have to wonder whether they would be okay with it, then don’t do it. Cheating is defined within a relationship, not by an individual.