A couple of things come to mind for me.
I'll have been married 10 years in June. We lived together for a year before getting married also.
*************THIS MY PERSONAL OPINION AND IN NO WAY MEANS FOR THE OP OR ANYONE ELSE TO DO EXACTLY AS I SAY*********
Have you and your wife sat down and had a heart to heart? Like let it ALL out, no matter if it hurts feelings. What worked for us was asking each other what needed to be changed on our behalf.
A lot of people may laugh at this, but my wife and I got into swinging about a year ago. Our sex life has been better in the last year than it was in 9 put together. We currently swing with two other stable, long term couples. Again it is just a thought, because we had gotten to where our sex life was pretty dull, it started improving right after the first swap.
How often do you get rid of the kids for a weekend? Maybe see if the kids can stay with a family member for a weekend, and then surprise your wife by taking her a couple of hours out of town to stay in a nice hotel somewhere. Take no phone calls unless it is about the kids, don't watch any TV, don't be texting everyone in the world. Make it about you and her only. Take her to a romantic dinner.
Kids play a big part in a couples happiness, don't get me wrong my wife and I love our kids more than anything. I would gladly lay down and die for my kid's sake any day, time, or place. BUT sometimes a couple needs a healthy break from their kids. I can only shed mine about 1 weekend a month, and that is doing good. Usually it is 1 weekend every 2 months.
Get a counselor, see if it helps. She may not fully grasp the fact that you are unhappy. To me in a marriage all the feelings should be out in the open all the time, versus holding it in until you can't take it anymore. She may just be in a boring old routine. Same thing everyday, my wife got like that and we had to break that dullness.
I know one of your main problems is lack of sex, but for my wife. All these things take effect on her sex drive.
She may cheating, I hate to put it bluntly. But from what I have read I don't think she is.