<human>: My friends broke up over the summer while we were away from university. It has turned out to be a pretty nasty breakup. Mark (23M) cheated on Julie (23F) with a mutual friend, Kayla (21F). Julie is now single, Mark and Kayla are dating. 

We are all…or we were all mutual friends and we share about a dozen more friends in our immediate circle. It has turned into a game of inviting either Julie or the new couple of Mark and Kayla. Mark and Julie will not even consider being in the same room together…and I'm ok with that. However, I feel like I am going behind someone's back when I don't invite the other, especially to events and hang-outs that I know they'd both enjoy. 

Furthermore, I feel like I am even more disloyal to Julie because she was hurt by the infidelity (that turned out to be long term emotional infidelity rather than physical) and I can't just write my other friend off for going about ending and starting a relationship poorly. 

How do I best go about this? Continue the segregation while trying to include them equally in different events? I really care about all three people involved in the "love triangle" and I don't want anyone to have hurt feelings over not being invited to this party or bowling or dinner…etc.

Can you give me the gist of the text in a nutshell?
<bot>: – Mutual friends broke up and our other mutual friends and myself feel disloyal by not including everyone in social events. What is the best way to go about this?