Not sure where to go from here

My husband and I have been married for 10 years and have 2 kids, 4 & 7. Marriage was wonderful but after kids has become more of a struggle. He feels we don't have sex enough; usually average 1 - 2 times per week. We have been to counseling and tried agreeing to sex every other day and that was working pretty well until he then got mad I was " just doing it because it was our agreement". We then went to "sex coupons" and that was not adequate. I will take some blame in that between a full-time job, running a household and being the more hands on parent, I am exhausted by the end of the day and sex is not on the top of my priority list. Add to that he becomes a real jerk to me when we don't have sex enough, which makes me pull farther from him. I just found out this morning that he meets up with a woman he met on an online sex site last June about once a month. He said it is a physical release for him and nothing more. I know the quick response from everyone is that he is lyng, but I do believe him. I know he loves me and our family, but his obsession with sex led him to thus. That certainly does not dismiss his behavior, but it leaves me confused as to how to move forward? I had always told him that if he ever cheated on me, it was over. But now that it has happened and I think of our two kids, I am not ready to throw in the towel. Anyone been through this and have advice on how to repair our marriage?

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