Ted what you are feeling is totally normal for it's hard to emotionally ignore all those years of marital history with a spouse, even if s/he is a selfish person.
As far as your children not wanting you to reunite with their mother, I would advice you not to take their advice. As much as you love them and would gladly take a bullet for them, it is your life and only you have the right to decide what you want from it, and if what you want is to rebuild your marriage then they will have to learn to respect your decision.
Standing your ground is indeed the way to go for she cannot be allowed to beleive that she can have two men in her life without paying the consequences for it. She has, for a period of time, the choice to decide whether she wants to come back and work to rebuild her marriage or divorce and move on with her life. I advice you to consider setting the following deal breaker pre-conditions before taking her back:
1. Agree to never again contact the OM. This should be done by her sending a letter or e-mail(preferably in your presence)
stating her intention to never again have any contact with him and for him to seize and desist form contacting her ever again.
2. Agree to implement with you a marital recovery plan that includes counseling with a pro-marriage professional like Steve Harley (from the
Marriage Builders Counseling Center or Penny Tupy (our resident MB coach, Cerri, and founder of
Save Your Marriage Central) as well as total willingness to implement
The Four Rules For A Succesful Marriage .
Dr Harley has stated that many times a BS(betrayed spouse) accepts the WS(wayward spouse) back without getting an agreement from the WS to agree to the above pre-conditions, that recovery never takes off. In other words, simply taking the WS back without the above pre-conditions, sets you up for a false recovery with a very likely continuation of the A(affair). I hope this helps you.