My assumption is that you are staying because of the kids. Is that so or are their other reasons? That is a noble enough reason for sure. It sounds like it could work very well.
The whole sex thing without her really being into it I find a bit disturbing, but maybe that's me. I don't think I'd be so keen in your situation and be looking elsewhere for love, companionship and connection. Sex isn't everthing for sure, and you could certainly have a connected relationship with your wife without it, but I would think having another or several othe relationships of a sexual nature would be more healthy.
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