As terrible as this sounds, perhaps it's time to sit her down and talk about the idea of divorce.
I don't mean threaten her. I mean try to have a serious conversation about where this relationship is going and what it's based on now - not fourteen years ago.
The fact that your children are the only part of your lives that keep you together is really sad to hear. The truth is, your children would find greater benefit in the two of you being happy and separate than together and miserable.
In the event of divorce, a great lawyer would be a good idea. I dunno where you're from, but many states have lawyers that cater to the needs of fathers in your predicament.
I don't think I need to be point this out, but - sex is not your issue, here. Not only have you grown apart physically, but there is no longer an emotional connection between the two of you.
Counseling has failed, and your wife refuses to communicate with you - maybe she will finally listen if you acknowledge how terrible you've been feeling lately and how serious you are about either fixing this, or ending it.
Remind her that you don't want to argue, and you don't want to throw insults around - you want to talk. If she gets heated, walk away and tell her that you'll continue the conversation when she's cooled down. Try to keep your temper, as well.
A happy marriage - a happy relationship of any kind - requires two people to be working hard. If one of you, or both of you, isn't committed it simply isn't going to work. Forcing it won't help.
Don't pass blame. Acknowledge her reasons for what has been going on between the two of you lately, and don't fight her on it - and hopefully she'll do the same for you. Really, this is a tough position to be in. Another attempt at counseling may help, and I would give it a try before any other options.
I hope that you guys can work things out, or can at least find some peace in your lives - together or not.
Good luck, in any case.