Some here might disagree, but in my opinion it would be OK to invite W along (if you want to). It sounds like she may have been fishing around a bit to see if you would invite her. In DR it talks about setting up activities like this and telling your spouse they're welcome to come along if they want to, IE, phrase it in terms that you're going whether or not they come along. That way it doesn't come off sounding like a date and there's no pressure for them to go.
