Any advice for how to handle this with a 15 year old and very soon (like in about a month) to be 14 year old?
I would be honest, albeit age-appropriate, with them. My kids were young adults, but even so, I told them that their father had been unfaithful and with whom, but I also reminded them that I'm a big girl who can stand up for myself and that I didn't need them butting in and choosing sides. It's best not to editorialize, but rather just give the facts. This is about your marriage, and it's okay for you to be territorial over it. And yeah... I practically choked on my own stomach bile, but our kids are literally made up of half mom and half dad, so I did remind them that their Dad loves them and that it's okay to love imperfect people. Attacks on a parent are basically absorbed as attacks on half of their sense of self, so it's good to let them know that we're okay and we can handle our business.
I know WS's don't like the kids finding out, but IME, it's impossible to hide something this big from them and when we try, we look like we're being arbitrarily mean to our spouse. Plus, kids hear through the walls as you know, and there's no way to know exactly what they've already heard. It's best that they know they can talk to you about anything and that you'll always shoot straight with them. For me, my policy of honesty with my kids trumped my fWH's desire to hide his dirt.
Right now, the ball appears to be in your court, so if you are of a mind toward R, it's a good time to be thinking about what you need to see from him in order to give him a chance. Bear in mind that no cheater is owed a second chance. He knew when he chose to cheat what the consequences might be. So, if you already KNOW that this is a deal-breaker for you, you're at no obligation to back down from that position. If you're not sure yet... this is a GREAT time to break up his romance with the OW. It doesn't feel very nice for OW's to get tossed under the bus when the wife finds out as you might imagine, but bear in mind, that even something which is THAT shaming doesn't stop a determined OW. She'll keep on trying to land her dubious prize. But in the long run, if R doesn't happen for you and your WH, she's going to KNOW that you were his first choice and it will undermine her security for all time.
So, if R isn't off the table, I would recommend that your WH write a "No Contact" letter, one that you approve. It should say that he doesn't want any more contact from the OW, that what happened between them was a mistake, and that HE LOVES HIS WIFE and wants nothing more than to repair his marriage. He should tell her than any further contact will be viewed as harassment and will be treated as such and through legal means if necessary. He should hand over all his passwords, close whatever emails and apps he used for cheating, change his phone number, download a family gps tracker, and anything else you need to feel secure. He needs to get into IC in order to find out what was so broken in his character that allowed him to say "yes" to cheating and lies. And when you're ready, he should attend MC with a qualified, hopefully Gottman-trained therapist. And... at any point, you might decide to bail. You aren't obliged to make any commitment you're not ready for yet, because feelings change A LOT in the 2 to 5 years it takes for healing to occur.
...he ended up in rehab due to alcoholism and his refusal to create any boundaries with his dad who was a charismatic womanizer and alcoholic (and also a third string NFL quarterback so just good enough to make WH's college football career never quite good enough. It's a whole thing and it's a mess and also very sad.)
Bear in mind that right now, you are NOT required to be thinking about what your WH's malfunction might be. It's not your job to diagnose him or to understand him or to fix him. But... if you're looking for some possible answers, you might try Terrence Real's I Don't Want to Talk About It. The dynamic you described between your WH and his father made me think of Real's treatise on "Covert Male Depression" and how unhealthy father/son relationships can cause problems in middle aged men. It's an interesting read in any event.
Remember that no matter how bad things get and how agonizing the pain might be... it's temporary and finite. It's a matter of time. Becoming proactive in your own healing can help. Taking excellent care of your body and putting YOUR needs first can help. So don't be afraid to be a little selfish just now.