My sympathes. It is hard work being married and a family but it sounds like you two had the conversatioon that can keep yours going.
Communication is the key. The fact that you were both honest is really a good thing. It sounds like you just need to do some nurturing and repair work.
Think about it, you answered your own question. You said you haven't had more than 5 dates in 2 years. Is that what your courtship was like? If you don't work at anything it will wither and die. So, this is your new job, both of you. Move forward with your marriage.
You will probably never be that stop you in your shoes "in love" that you were at first. That fades for everyone. if they say they have it they are lying. What you can have is a renewed even more deep and trusting connection and yes, love, and now is the perfect time to do it. Marriage is a series of adjustments like this. (I've been married for 17 years, together for 23)
First, make a pact to be positive with each other in all you do or say. Then sit down together and plan out when you can reasonably spend time alone together. It may be one night a week after the kids go to bed, or can you find someone to watch the kids while he has his break at work? Lunch? Have a date, just to talk like that each week. On weekends or when you can, schedule snuggle time. You don't have to make love, just relax and talk, get close. The rules are that you can't talk about any family business. none. Just about what's new with you or about whatever you used to talk about before kids and family.
When you feel you are ready for it schedule an overnight out if you can. You may think you can't afford it, but can you afford to loose this marriage? Do it. And relax about the sex. Closeness is what you both need, just with a little emotional intimacy groundwork before hand.
As for you, lead by example. Show him how much you love him. Say it. Leave him little notes , emails, text him. Rub his back just a little as you say it. Make his favorte foods, pick up a magazine he might like...just little things. You will know what will work. Let the world revolve around him for a little but...and then if he's paying attention, he may start to reciprocate. Sometimes guys need to be shown the way without you actually letting them know that you are showing them.
Be patient. Sounds like both of you are under a lot of stress. Realize that anyone under those conditions would crack. Trust that love and trust will get you through. But actively show your love, daily, in little things and I think he;ll get the message and calm down, and be your man again..but better.