@SweetT,
What I would do?
You are already not with him, emotionally, probably sexually so start to live for yourself.
Spend the next few months re-gaining who you are, the dreams and goals you had before you both got together, coupled with new ones, where you want to go "now" with your life.
Start searching for groups you can join, classes you can take, gym things that you like.
Gaining independence, is the first step as it will be a long and lonely road once you are travelling on your own.. However, already being independent will mean you will know who you "now" are and where you are going, when it comes time to walk away.
Also start spending more "fun" time with your children. They will accept things alot easier if they have a Mum that is happy in herself and shows it with them..
You are only lowering yourself by having an affair and risking emotions that you can't cope with yet...
A new you, is a better option ...