Only you can decide if you want this trainwreck to continue.
Oh, and your wife seems to accidentally get pregnant an awful lot. Perhaps you should consider a vasectomy - or at least work with her to get measurably more reliable birth control. A lot of your life decisions have been made by what's going on in your pants. You have been letting life happen to you, and I mean both
It's time to stop that.
Counseling is often a good idea. Not necessarily to repair your marriage, but to think about and plan what's going to happen next. You may also want to think seriously about the economic consequences of upending your marriage. If you two can't afford one household, then you're definitely not going to be able to afford two.
And lastly, no matter what happens, don't stay together because of your kids. I guarantee your older child knows what's going on, and your younger has an inkling that something is not right. If you do decide to stay together "for the sake of the children", then it's another case of letting life happen to you.
You're the grownups in the room. It's time to take charge of your lives -- whatever direction they lead to.