Personally, I find it's the kids that usually end up suffering when you stay in a relationship because of them. They're not stupid. They know more than most parents give them credit for and hear more than you think. They can feel it in the air. 1. you're giving them guilt that they have no request for. 2. You're leading by example. Do you want them to be in healthy, happy relationships or do you want to pass off the thought that it's okay to cheat and be miserable in a relationship which lacks respect and love?
I know, that's kind of a simplistic break down of it all but that's what it's felt like and been for me. I was married for 14 years. My ex cheated on me but we struggled through. He had some health issues and needed looking after, we had some family problems and needed to be strong. At the end of the day, I realised that things were now stable and I was deeply unhappy. It wasn't a relationship, it was an agreement of convenience. It took a very long time for me to weigh it all up. It was the hardest decision I think I've ever made. I didn't do it for anyone else aside for myself, My ex and my kids. We all deserved better. I'm not going to lie, it hurt, it hurt like a bitch to walk away but in doing so everyone could start to heal. My ex is still on the mend, we all are. The kids are happier as am I. I'm in a healthy relationship and the kids have a stress free life. No more arguments, no more pretense. An honest, forthcoming and happy home. They no longer have to pretend at happy families just to make their parents feel better when the whole reason for that was that we, as parents were pretending at happy families to make them feel better. It fooled no one and taught my kids that this is how a relationship works. It isn't.
I'm afraid no one can give you any answers. You must seek them out yourself and do what's right by you, your ex and your children. Mostly your children. Give them more credit for seeing through the facade. Sadly, they're not babies anymore and are more aware than you think.
Even if it's something as simple as holding hands with your partner or a kiss on the neck, sharing house hold chores or taking time out of your day to go with your partner to a doctors appointment your kids will see what a loving relationship looks like. You can only hope that they don't mistake a healthy relationship with is what essentially is lip service. Everyone loses in that scenario.
Best of luck with this problem. It's a bastard of a situation to find yourself in and I wish you all the very best for you, your kids, your current love and your ex. It's a mountain but I'm sure you'll conquer. xxx