Vik, there's a lot going on here. I'll start with the parents.
I'd say the best thing for you to do is NOT MEDDLE with their relationship. If her parents come to see her that is between her and them. If they ask you anything about your relationship you kindly and firmly say to them, "Thank you for your concern. I appreciate you wanting to help, but I think right now it is best for me that I keep some of the details between W and I private. I hope you understand".
Stick to that. Do not draw them in. Do not pretend they are your allies, and do not treat them as the enemy. You may need to be a broken record and repeat your stance.
If W asks you to relay messages to her parents take a similar stance. "W, I understand your parents being here is a stress to you. I think the best thing I can do is step back and allow you to manage your relationship with them. I don't wish to be in the middle".
Regarding childcare and exposing your child to OW - these will require conversations with W and I'm not caught up on your sitch enough to know how to best advise. When in doubt - do nothing and step back.
