No. Don't do this. This is not the time. It will definitely be backhanded pursuit and she will see it as manipulative no matter how genuine your actions might be.
Just let it go for now. What I did with my in-laws (and I currently am and was always on excellent terms with them) is the following. Big caveat here is that I have 2 kids who are very much attached to them and they will always be family to my kids, regardless of whatever happens.
So, I said this to them, "This is a difficult time for all of us. Just out of respect and space, I won't be reaching out to you for anything. If there is anything you want to talk to me about, I am more than happy to connect with you. You are family to my kids and will always be and I will make sure that you have access to them and that your relationship with them is not harmed."
And I have left it in their court of what they wanted to do.
I have interacted with them when they have come to town, but I haven't reached out and they haven't either. I am not going to speculate why they haven't reached out to me, but that's whatever.
I make sure though that the kids can reach out to them if they wanted to, and that I give them a call for bdays and other important events so that the kids can wish them and talk to them. I want to facilitate their relationship, even though mine with them is very limited.
In your case, you don't have kids right with W? So, I don't see any reason for you to reach out.
