@thetwister If you as you search your heart you decide that what serves you best is staying, turning a blind eye to the affair and biding your time and positioning yourself well for a split when the kids are older and you're able to earn, AND you feel you CAN do that with your sanity, your emotional health and dignity more or less in tact... If that's the path you choose the here are some considerations:
1) Maybe set some boundaries for yourself. Under what conditions would you then switch from this plan to leaving? How many years? Whatever parameters you need to know that you're in charge here, and you will be taking care of yourself no matter what happens.
2) Following on from item 1. If a long exit is what you choose, do have an emergency exit plan in place. So talk to a lawyer, find out how it works, what do you need to have in place so that you can pull the trigger if that should become the right thing to do?
3) This last point is really going to depend on you, your spouse, the culture you're in- it might be a total non-starter. If you're living inside a religious, authoritative culture, or any culture where men are especially threatened by women and where women tend to be controlled/directed, or if your husband is easily threatened by women then don't do this.
But, if it would be SAFE to do so, could it possibly be helpful to give the appearance of coming to an arrangement together? That is, you keep your plans to leave to yourself, but you tell him you're okay with him getting some of his needs met outside of the relationship. Let him know you know and that it's okay with you.
In my culture this would not be a radical thing to do, but I understand it could be in your case. Here's the benefits - less lies, less secrecy, less distrust, less isolation between you both. It could (depending on if it would be safe to do this) actually make him more predisposed to be nicer to you, and it would correct some of the power imbalance. You would have more power in this scenario- you aren't a victim, you're making your own choices. You would keep it private between you, but between you you could at least be truthful with eachother, less games.
Again, you keep your cards close to your chest and make your plans to leave on terms that work for you, and get that additional time in with your kids while they're small, but take the temperature down a bit between you in the meantime so you don't have a paranoid spouse worried about getting caught?
Or maybe not- it's something I know some women have chosen to do, but it might not be right at all for you.