Hi Burningwater,
Welcome to SI. I'm so sorry you have reason to find yourself here but I'm glad that you found us. We are a wonderful resource for commiserating about how difficult this is (it's hard to imagine the breadth and depth of the devastation infidelity can cause unless you've been through it yourself), providing support, and comparing experiences and strategies. I know this all feels incredibly unique and specific to you, one thing you will find the more you read here is how similar the experience of betrayal can be from person to person, and perhaps more importantly, how similar the 'script' wayward can seem to follow in the aftermath of D-day (discovery day, or the day that the affair was discovered).
A few things about your story stick out.
1. You appear to be blaming yourself and your failure to notice your husband's struggles for his affair. Please stop this, immediately if not sooner! None of us are perfect spouses all the time (or ever), but that doesn't give him license to go outside the marriage. I get it, it's a way for you to feel a sense of control during a time where everything seems to be in flux, but that's just an illusion. The reality is that nothing you did or didn't do caused your husband to cheat. NOTHING. You can own your part of any marriage issues, but he owns his cheating 100% - full stop.
2. I don't know how the 'kissing in the park' thing was discovered but your husband has only admitted what you already know and nothing else. That's not a good sign. One thing that's common to 100% of cheaters is that they lie (to their spouses, their affair partners (APs), and to themselves. The number one lie we hear here is "there wasn't sex" followed by "okay, it was sex but it was only once". I'm not saying its impossible that your spouse was being entirely truthful about this and you are one of the luckiest people in the world that you stumbled on this the first time that it ever happened.... but what is more likely is that there is more to the story. There are usually a million teeny line crosses before things get physical and things get physical, things usually progress quickly especially if there is opportunity. I say this gently, but both you and your husband should likely get tested for STIs to be safe.
3. The AP (affair partner) is a coworker. I assume that means that he still sees her regularly. If you want to reconcile your marriage any continued contact between your spouse and his AP needs to be an absolute "no go". You will not be able to feel safe in your marriage with her in your orbit, no matter what he's telling you. Please know I say this as someone whose spouse also cheated with a coworker. Is your husband able to change jobs or work locations? How can you be assured that they are not seeing each other? Keep in mind, their relationship was obviously able to progress to this point in their current arrangement.
4. Speaking of AP, is she married/in a relationship? If so, I highly recommend notifying the OBS (other betrayed spouse) as soon as you can (and without telling your spouse about it first). It will blow up her life a little and will mean that her attention is focused on her spouse rather than trying to woo your husband back. I made a lot of mistakes, but telling the OBS almost immediately was the best thing I did post-d-day. It meant that my husband and his coworker other woman (COW) were not able to get their stories straight and I ended up getting a lot of information that would likely have been minimized or obfuscated early on rather than. I'm a firm believer that you cannot forgive or heal from something you don't know has happened. New disclosures will set your healing back to zero and so if there is more so much better to learn the whole story NOW rather than months or years from now when you thought you were reconciling. Looping OBS into the whole thing also meant that there was an extra set of eyes watching AP going forward which provided me some comfort.
5. The way you're feeling right now is incredibly normal. If you weren't feeling this way I'd be concerned for you. 2-5 years (YEARS!) is the average/normal time estimate it takes to heal following betrayal. I know that sounds incredibly dramatic and overwhelming at the moment but it's true. There is no skipping steps in any of this You may feel that he's more likely to "pick you" if you do your best to swallow the way you're feeling and push it down, in the hopes that things will go back to "normal" (we call this "rugsweeping" by the way), but I promise you that doesn't work. Not dealing with this wont actually go away or resolve. Your feelings and fears will fester and get bigger turn to resentment that will be present all the time and will impacting every part of your life. He will have no one holding his feet to the fire and will not actually have any motivation to "do the work" necessary to become a safe partner and fix the things that are broken in him that left him vulnerable to cheating, which will always make him vulnerable to doing it again. He will eventually become irritated that you "cant seem to let this go" and eventually become indignant when you continue to bring it up. Rugsweeping may seem like a good idea in the short term, but I cannot tell you how many people who do it find themselves here decades later still absolutely haunted and torn apart by issues that did not got properly addressed and did not magically go away on their own.
6. Further to the above, what is he DOING going out with friends mere months after d-day. He just got caught cheating! His entire world right now should revolve around trying to comfort you and make sure you feel safe. There is ZERO benefit to you in being the chill, lackadaisical, "cool girl" wife right now. You already played that role and this is what it got you. You need to have a million hard, uncomfortable conversations. You should be unapologetically making new rules and boundaries that make you feel safe. Things like zero secrecy around his phone should be a non-starter. You should have access to all of his accounts and passwords. He should be notifying you of any contact at all from female friends or colleagues. If he objects to any of this, he either doesn't understand what he's caused, or he doesn't care.
7. Not only is it normal to not trust him right now, it is SMART. You are right not to trust him at the moment. Whatever he says, this wasn't a momentary . It was a lot of big and little decisions and moments over time where he knew he was pushing boundaries but happily creeped over them. At the very least, he spent months messaging and opening up to this woman behind your back at the expense of intimacy in your relationship. Trust takes a second to break and a AGES to build back. The only thing that works is transparency and consistency over time.
I'm sorry if this sounds like a lecture or an over-the-top screed when all you wanted to was a hug and for someone to reassure you it was going to be okay and that you could go back to the life you thought you had. Unfortunately your old marriage, is over and it isn't coming back. Building a new marriage is possible if both partners are committed and all in (i'm living proof of this!) but that is not going to happen overnight. Check out the healing library, there is a lot of really useful information /articles there and read the stories of others. I think you will be surprised at how much of yourself and your husband you see in them.
Best of luck and keep posting.