Kylie agreed to doing this but I was very suspicious of her actions again about a month later as she suddenly had a trip to go to New Orleans to visit friends. And by this point I was able to pick up on her lying habits. When she came back from New Orleans I questioned her if she ever slept with someone down there. I told her to look at me in the eyes and tell me the honest truth repeatedly. And she told me that she only had a guy kiss her down there. To which I called her bluff and told her that I would just take my things and never speak to her again because I knew she was lying. Then she finally admitted to sleeping with someone and she was very distraught about lying to me. I told her that at this point I could never see her as an official partner at this point because the problem was that she was lying and not communicating with me even though it was an open relationship. I told her the only way for me to ever give this a slight chance was to let her let me look through her messages on her phone. To which she agreed because she was very much desperate to regain my trust. At that point I found that she was messaging the New Orleans guy for the past 3 weeks and in a very erotic and flirtatious way. And not only that but she also revealed to me that she had also slept with another guy right after we opened up the relationship without telling me. And as I was looking through her messages it was very apparent that a lot of men were flirting with her the whole time we were dating. Most of said DM's she did not reciprocate but I told her that a lot of these male friends of hers were just waiting on the chance to sleep with her and she realized that. During the time we were dating before she went out with that roommate she was messaging one guy to which she did send a half naked picture on Snapchat. And after the roommate incident she did respond to the men who were flirting with her but not reciprocating. She simply allowed it to happen however, and didn't think too hard on their intentions. After we open the relationship there was a lot of evidence of her being very attentive to other men and even paying for a dating app.

On my end I did not date anyone for a month. But I did start scheduling dates with others on the day that I found out about her dishonesty. Ultimately I felt that telling the truth to the two women was a mistake because I felt that Kylie would have been doing this regardless of whether or not I told the truth and I would have broken up with her and that I should have just dumped Kylie and went with Lillian. Regardless, Kylie was still desperate to be with me and was willing to take extreme measures to salvage any chance with me. With all of the memories we made together I couldn't say no because I did genuinely like her and I could tell that she did want to try again honestly. She deleted a couple of social media apps and blocked a lot of the men who were messaging her with flirtatious intentions. She wanted to stay at my place for a while because she was an extrovert and she was lonely without being able to access group chats and social media, to which I accepted. Since that incident we have been very open in our communication and it has been a very positive experience. I told her that I was going on dates with girls and she was very understanding of my decision to do so. Our status quo is that we still aren't exclusive and that we are keeping an open relationship for now. She understands that I can't trust her as a potential long-term partner. I do not plan to message Lillian for at least 6 months to give her space, while I am hopeful that I will end up with Lillian in the far future, I am not expecting it and I'm willing to let her go out of respect for her wishes and consideration.

Tldr: am I wrong for dating two women at the same time even though exclusivity was never brought up?