Don't you have an attny? If so provide her with the name and address of your attny so the papers go there. If you don't have an atty get one.
I would say something like this:
W: The contact information for my legal counsel is <insert info here>. Any documents pertaining to the divorce should be sent directly to him/her.
If you choose to rip up the insurance card that is your choice however it does not remove you from my plan. Your options are as follows: obtain your own health insurance plan in the next 10 business days so I can remove you from mine as per company policy OR contribute to the monthly payment until the divorce is finalized. Which do you prefer?
And, I see no problem in letting her know your legal counsel is already aware of the actual date of separation.