Dear Missing It:
You show wit, insight, compassion, and your children's best interests -- I think I can help, or at least, I've been there.
Kids Get in the Way
Basically, you are right when you say other aspects of your relationship are suffering. Frankly, that's the crux of the issue here. The kids are clearly in the way. Your wife seems to have defined herself as a mother first -- she's staying at home. That is very important for your young children, but she'll find eventually that the role can be limited in terms of self gratification. I don't think kids take the place of husband, career and self growth.
My guess is that the degree to which your children have taken over your lives is a shock to both of you. You probably started missing your wife's attentions when she was pregnant the first time. Since then, she's had to cope with her body changing, the constant demands of infant and small children, and with her own hormonal changes as well. It's not uncommon (take it from me!) for women to want sex much less when there are young children in the house.
Desperate is Not a Turn On
Ironically, because you are now playing second or third fiddle to your children in your wife's attentions, you probably want sex and real connection all the more with her. And, your desperation (or neediness) is probably not a big turn-on for her. In short, it quickly becomes an incompatible system.
Are you wrong for wanting sex?
Are you wrong for leaving your wife for sex?
You guys have to look back to what got you together in the first place. If it was primarily a sexual connection, then, yep, I think you've got a problem. Sex and parenthood just don't mix too well. Did you ever catch YOUR parents in the sack?
Get a Hobby
So, my advice is go back to the therapist and really talk about what the fundamental attraction is between you two. See if the compatibility has been compromised by other demands. If that's true, see how you can get the magic back. It may be that your wife is not interested in magic...if so, try surfing...that's what I did.
It's interesting to me that the amount of surfing I do directly correlates to the amount of sex my wife and I have. I'm not being silly. During this phase of your kids' lives you may have to find other recreational activities that give you the meaning and connectedness that sex brings. For me it was surfing, for you, maybe it's riding a motorcycle, hiking in the wilderness, joining a soccer team, who knows?
My advice is to sort out the real relationship issues from the issue of sex. Sex reflects the deeper goings on of the relating you're doing with your wife.
Can that connection be repaired and improved? If it can't don't feel guilty, you are at least looking at the real issues and not just the sexual ones.