Only you can judge the interactions between W and your mother. But from how you described it you handled it pretty well. Validating with W is one thing but standing up for her could show her again that she is the most imp person in your life. I don't mean fight her battles for her or to take sides categorically but saying something to mother afterwards (even now) could be a good thing. You may feel better and won't harm W opinion of you. This is just my opinion and as often here is tinged with how I would think n the same position.
R 25 years M 14 years S11 & S13 Working on it alone since Oct 2014 M in trouble a lot earlier (~2 years) Feb 2016. 1st R chat in a yr. Next R chat Aug'17 Still together