The emphasis has to be on whether or not there is enough in your marriage to build on going forward. The advice you are reading about is likely referring to this fact — the only question is if the marriage is viable and worth going forward. I would be direct and discuss this with your wife. Let her know how you feel and that it needs to change. You might be surprised at her reaction — often the other spouse is just as unhappy as well. Talk about the options. You could work on trying to make it better by yourselves (not usually very successful) you could separate, or you could go into therapy. Since there are children I would suggest the latter so you have a chance to either work on the relationship or end the marriage in a way that disrupts the children the least.
Acting out with the affairs is likely to continue if you don’t deal with this more directly. This will create more problems downstream than if you try to deal with it directly.