If she has cheated numerous times then I fully understand why you would do this , the relationship must be bad and we all need someone. Please think about the outcome though which is not always apparant when you are being carried along with the moment.
You are putting yourself in a worse emotional postition by doing this , you deserve better than a serial cheat so setting yourself free to find a single yes SINGLE woman will work much better in the long run. Also it won't be long until the wife susses the emails as before you know it you will be spending hours on the computer. I can understand where you are coming from where the children are concerened and don't want to leave them . That shows what a lovely person and father you are. You don't deserve any more crap so don't put yourself in a position where you will recieve more. bless ya hope you sort this out for you and the kids. good luck