The question is, how do you really feel about your marriage? Bored and unhappy but wouldn't want to lose it, or reached the point of wanting out? (And since you've got kids, I'd at least say you should be talking to him and trying to work things out before getting to that point)
Imagine how you'd feel if your husband found out about the affair and asked for a divorce. Do you feel sick, awful, terrified? If so, then you still feel you have something to lose – don't risk it, it will never be worth it. Break off contact with the OM and try and rebuild your relationship with your husband.
On the other hand, if you imagine that and feel relief that you'd be ending a relationship that's already done, then do the right thing and leave, rather than pursuing an affair while your husband has no idea his marriage has ended.
I get that you feel like you can't choose between them – unfortunately, you have to. As has been said a dozen times above, trying to have both will only end in a world of hurt for everyone involved. Could you face a lifetime of your children knowing you cheated on their father? The longer this continues, the more chance that you will get found out, and you'll never get back what that will do to them.