Its not your wedding so its not up to you, period.
If she is invited by SIL then fine. What a golden opportunity to DB your ass off! Get a hot date and dance and prance in front of W at the wedding and have fun. You're right that W will likely be uncomfortable with the cool reception she gets from some of your family. So be it. Tough for her. If you have a PMA about this situation you could actually have fun with it. But you make the call.
