Hey Jim_cs, sorry to hear about your situation man, it's horrible to feel helpless. I don't know what the best solution for you is, but I respect that you are staying in this far from ideal situation for the sake of your kids. You sound like a good father.
For their sake and your own you have to maintain your mental health and some sort of happiness in life - I think it would be hard to really be there for your kids without taking time for yourself. It's certainly not bad or wrong of you to want sex and intimacy with your wife, but in this situation neither is it a bad or wrong alternative to seek some aspect of that through punting. You gotta stay sane man. Maybe there are guys out there who can lead rewarding, fulfilling lives without sex, but seems kind of pointless. If your wife can't respect or understand that (and unfortunately many don't seem to), well you have an alternative.
As far as the overall situation - remember, you can't change someone else if they don't want to change. You can only change yourself and your situation. I don't know enough about you or your situation to know if you could or should change yourself so that your wife's attitude to sex and intimacy with you will change - I kinda suspect not as it seems like the issue is probably with her. Well, at least 50% of the issue, and sounds like she's not willing to work on her part. But if there is something you want to change with yourself, something that might improve how you feel or your situation, you have the power to do that.