So you realize you are cheating on Tom, which I guess is some level of self awareness. Imo there's no separation of emotional vs physical and one is better or worse than the other. Unfaithful is unfaithful. You are deliberately engaging in romantic intimacy with someone other than your partner. Your own behavior has shown you are incapable of keeping things "truly platonic" with Kay. If you want to be in a romantic relationship with someone else imo you have to cut way way way down on time with Kay, perhaps even a period of no contact. And Kay has shown with her behavior she's probably not really ever going to take the plunge and fully and openly be with you. I even hestitate to call her your "ex" because yall really were never together by the info in this post. Yall had a messy situationship where Kay was cheating on her partner. Just bad all around.

Even if you ditch Tom and decide to keep the friendship with Kay what are you going to get out of that but more pain, longing, and frustration. Sometimes there's just people you can't be around because the timing is never right. It sucks but it's how we react to these times that shows our character. And right now both of yall seem to be so stuck in the weeds of your situation you can't zoom to see how it makes both of you behave in really bad ways.

I mean is your bf the type of person who judges people by their families? Is he from a culture that holds family "behavior" or "appearance" in high regard? If he's not then this feels like your own shame over your father's behavior spilling over into anxiety about what other people will think, when I think most sensible people would see that and go "ah what a shame your father is a jerk, must've sucked for you" and wouldn't use it to judge *you* as a bad person. You're not responsible for your father's bad actions. In fact it seems you condemn those actions quite consistently and seriously. Why not just open up to your boyfriend, since you say it's a "serious long-term relationship." So what if he sees that your parents are dysfunctional? As long as the two of you are treating each other well and it's not affecting your relationship, all it does is give him a little more information about your upbringing and in fact could be helpful in the future for giving you both context to be better communicators.