I am very sorry for what you and your wife are going through and am equally upset that the company is dicking you around on this. It is none of their business other than ensuring that they are adhering to the letter of the law. They have no right to call her doctors---period.
This may be none of my business but are you the only one who is available to take care of her? Are there any other family members or close friends who can pitch in and help out on an occasional basis? Working may help to take your mind off of what is happening at home and in no way diminishes the level of concern that you have for her well being.
While I can understand your position that you should be able to use FMLA as needed during the week, I can understand the companies position that you should be able to work on Saturday, as needed.