I would not reply to SIL's nastygram. There is simply no benefit to you whatsoever to do so. Your ego does not need that low grade food.
I would not talk to W about SIL's letter. Again, no possible upside. What do you think the chances are that W agrees with your position and sides against SIL? Zero. And she'll throw in something else to irk you even more, and you'll be fighting to contain yourself.
When you see a hornet's nest that is clearly labeled "HORNET'S NEST", and you happen to have a stick in your hand, resist the urge. No good can come from this.
