Sorry to hear that you're going through this Sarte, and sorry to hear that you kids will be going through it as well.
I can understand what you're trying to accomplish here, but have you thought about just being honest with your family that you're getting divorced because your wife cheated on you and you are unwilling to stay married to her? I don't get why you need to pretend anything other than that here. You can still choose to live together and to be working on rebuilding your relationship and rebuilding trust and be honest about it (or choose not to). Why lie to your family when you don't need to. It seems to complicate a painful and difficult life circumstance, IMO.
I can totally get the thing about being worried about how the kids will be raised at your ex's house (if her partner is disciplining them, etc.). It isn't easy going through a divorce, but I believe that you will do your kids a favor by actually creating a healthy, trusting relationship for yourself. They will learn from what you do, not what you say. If your relationship is a sham, they will learn that is what a relationship is supposed to look like. Do the right thing and be honest with yourself and take on raising these kids right. Find someone who will do it with you, and be happy. Why waste your life in a relationship that you're not committed to?
It sounds like you've resolved that your wife is not trustworthy, and that divorce is the route you want to go. Why not just sell the house, split everything up, divorce on good terms, and work on building your relationship with the mother of your kids as just that - the mother of your kids. She is going to be in your life whether you like it or not, but I don't get the desire to pretend that you're married "for the kids sake" when you are not.
I agree with those saying to get the paperwork done & finalized while everything is still amicable, btw. No telling how things will change if it starts to sink in that getting divorced really is getting divorced, regardless of whether you want to make believe otherwise.