It sounds as if you are both emotionally out of the marriage, your wife certainly is showing interest in other men and has cheated emotionally if not physically. I understand that you love your children and do not want to be seperated from them. But is it actually good for them to be experiencing the atmosphere ay home where their parents are distant with one another. If your wife has tried twice to find a lover then she is likely to keep trying. Although you feel that you can remain together for the present, things change. What if she does find someone who is receptive to her advances? How long can you live without an emotional or physical connection? It is natural to want to be loved.
I would speak to a solicitor who specialises in family law and take independent advice. If you have been involved with the children from an early age and work from home then your rights may be greater than you imagine. The main issue is that your wife does not work and does not appear to want to either so that unless she can find someone who is willing to keep her in the style to which she has become accustomed she will be fighting you for every penny she can get.
Whatever you decide it is important that the children know that you love them very much and that nothing happening between their parents is their fault.