Are we talking about an emotional affair where they are in the early stages, or do you think they have expressed I love you's and are sleeping together?
It is VERY hard to expose emotional affairs... they often get laughed at...
Until he's actually doing something physical with her, most people don't think its a problem... They never think these things are a problem until its way too late.
If your children have indicated they don't want to be around her and the STILL insists on keeping her around them, THEN i would get a lawyer to draft up papers to deny him access to his kids unless he's visiting them in YOUR home and they are being supervised... without OW.... your H can't take them anywhere on his own unsupervised. I would push for htat, if your SONS don't like her either... that's a HUGE red light... and I would argue cause for supervised and limited visitation.
THEN go protection phase and shut the husband out of your life physically and emotionally.