If you're only in the M for the sake of your children, don't succumb to a life of misery. If the kids are the only reason you're staying, then begin connecting with your W through family activities. Look at it this way - your children will benefit greatly from parents who show them how to be a loving couple.
And why not start with the simple things your W is asking for? The things that don't involve physical affection, like simple conversation - current events, your day at work, her day at work (or home), etc. Why not ask her about her aspirations and encourage her to go after them? You said yourself that she has been a very supportive W to you. Why not return the caring behavior(s)?
Thank her for the little things. Taking out the trash, doing the laundry, preparing dinner, whatever she does for you. If you can act appreciative even before you feel it, there's a good chance that loving feelings will follow. Act as if your R is as caring as you'd like it to be. You may find that these small attitude adjustments could lead to more positive and permanent pattern of interactions with your W.
Was there ever a time when things were good? What was happening during those times? Please don't come back and say there weren't any at all. There had to be. You just have to break down that wall to see those moments.
Oh yeah, and above all else, your W DOES deserve honesty. If the shoe were on the other foot, you'd feel the same way.
Getting over a painful experience is much like crossing monkey bars. You have to let go at some point in order to move forward. ~ Joseph Campbell