I'm not going to begin to suggest that I have any real clue how to handle a child with the needs that yours has. I am certainly not suggesting that you do something to put his health or well being in jeopardy.
You did say this: This is the paradox. So, when I started doing LRT, I spent more time out of the living room, playing with the kids, reading books etc. and that just made W even more annoyed. W made pointed remarks about how I was now spending more time with the kids, why was I doing weights etc. and why didn't I do that before (I did, but I spend even more time with them as I don't know when you're going away).
If I'm reading this, you're equating "got annoyed" and "made remarks" with not working, correct? The way I read it is that you made a change and she didn't understand it so she got upset. Of COURSE she's going to get upset. You stopped being reliable ole Huddy, chasing her around. In my opinion, you cut it short before really letting the new dynamics take hold, and now you're back in the same dance trying to "please" her.
I could be way off and if so I apologize. Hopefully someone else with more experience will chime in.