I would suggest that you let him know that you know, and show him that you can do it without screaming, begging, crying, etc. In other words, A MIDDLE GROUND between the passive-aggressive approach you've tried so far.
Does that make sense? So far it seems you've swung wildly between aggressively screaming and crying at him, to passively condoning his continued infidelity.
Neither of those approaches will work.
What DBing is about is letting them know that you are aware of the infidelity, that you are NOT okay with it, but that you also know that he is an adult and that you cannot control him. If there are aspects of it (say, text messaging her in front of you, or coming home after a certain hour) that you find unacceptable, then establish those as your personal boundaries, and then MAKE SURE YOU STICK TO ENFORCING THEM. But beyond that, "drop the rope" as they say. Work on YOU (that's what GAL is -- "Get A Life"). Mentally, you move on. You let him know you love him, and this is NOT what you want, and that you are categorically NOT OKAY with it, but you STOP working on the relationship with him, and you work on YOU and your kids, instead.
My bet is he'll respond to that.
Put it this way: think of those two precious little girls. I have two daughters also, about that same age apart, and they are now 21 and 19. How would you counsel your oldest daughter, 18 years from now, if she came to you with this same problem?
