Your story is sad, but unfortunately, its pretty typical.
I know you feel you were duped - by a bait and switch type of tactic. Please try to believe that your wife did not consciously do that to you. That may be how the results feel to you, but she did not set out to trick you this way and is secretly laughing because you bought it.
Women with low sex drive often do not know what they are missing, and because of that, they don't know how to manipulate someone with sex. Does that make sense? If they knew due to experience, that sex was something that makes them happy and warm and fuzzy, then they would know what they were doing to their partner by not having sex with them.
Also, women in this society are totally encouraged to feel it is normal for them to not want sex, so women with low sex drive really hold on to this societal approval within themselves and they don't really question it.
Not until they end up reading more, learning more, going for counseling, or sometimes something more drastic - their husband is about to leave them - do low sex drive women realize they need to change their view on things.
I think in a perfect world, all the low sex drive people would be married to each other, and all the higher (or just normal) sex drive people would be married to each other - - and then everyone would be having sex at the rate they would prefer.
But as you know now, you didn't make sure you and your wife had matching libidos before you both said "I do", so you need to take your part of the responsibility for that part of things. Also, as I said above, trying not to believe that she consciously duped you will really help your sitch.
Have either of you read the Sex Starved Marriage yet?
I'm glad you are (or have) tried to do well with the non-sexual touching and so forth. To me, from what you've described, your wife is going to need some "in your face" type of catalyst so that she knows just how unhappy you really are. She doesn't need to feel she is 100% the cause of your unhappiness, as that wouldn't be fair to her. But she needs to know that the lack of sex in the relationship is one of the causes, and that she has a responsibility to try to find a happy middle ground with you on that part of your relationship. I would intiate a talk along the lines of "honey, I am not happy. I would like to be happy with you, and I will do whatever we need to do to get us from here to there. Would you consider marriage counseling with me so that we can fix this?" And then don't back down or get into other issues if she tries to deflect. Just remain on your point.
I am very sorry and sad to hear one of your children has cancer. I hope that works out for the best and everyone is ok. For that reason alone, I would think you and your wife may need marriage counseling, to deal with the pain and grief of the situation.
There is hope for women with low sex drive...but you need to push her into action. I hope my advice doesn't step on anyone's toes as I am new here! Good luck.