Solost, I've been following your thread but haven't posted yet. You sound as if you are doing a fantastic job of holding family life together, and I'm sure your children appreciate everything you do for them.
Though I haven't been in your position, the posts from those who have seem to be unanimous in suggesting you act urgently to protect the financial/ housing security of you and your children. This is about more than your relationship with their father; you now have to assume that you could end up being wholly responsible for their care. No matter how much your ex says he loves the children, no matter how often he visits, he has proved that he was completely willing to ditch their happiness and security for the sake of sex with another woman. However good a father you think he is, he has already shown you all that the welfare of the children ranks as a lower priority than the desires of him and his other woman.
I think that you probably need to act fairly promptly about telling the children- it should come from both of you together. Another poster suggested saying that Daddy has left because he wants to live with another woman who he prefers to Mummy, which is honest, and detailed enough for children. However, it's very likely that they'll ask why he doesn't love them enough to stay, or something similar. Your ex has to man up and take responsibility for answering this- he owes them this. Don't allow him to shirk this and leave you to try to explain, and don't let him and OW trot out some fairy story. For the children's sake you need to take control of this one.
As somebody else pointed out, the OW has no interest in caring for your children- if she was at all concerned about their welfare she wouldn't have started an affair with their father. They are her meal ticket- the more access Ex and OW have to the children, the more money they get to keep. I'm not suggesting for one minute that you deny the children access to their father, just warning that you need to be very careful what you agree to. They have a 4-bed house to buy, don't forget- they won't want to be paying for you and the children to remain securely housed and maintained.
Seeing a solicitor promptly would be wise- you don't have to tell ex that you're doing it (and what on earth do you owe him in terms of honesty anyway?). I understand that you don't want to antagonise ex while terms remain apparently friendly. However, you need to consider two things here. One is that you cannot rely on your ex to put the best interests of you and their children first, because he has already proved that he is not willing to do this. Secondly, he and OW have probably already sought legal advice. They might well be discussing how much longer they can keep you sweet and delude you that things are civil before doing their best to take as much money and security out of your marriage as they possibly can.
As an aside- before I read your username capitalised your name as SoLost, I was reading it as Solo St, as in somebody walking a new road with newly-found independence. I wish you the best of luck.