D.B.
Added - Barb gives you good advice, especially about your birth plan. Just remember, the hospital can change their rules any time, and just because they allowed something last year, doesn't mean they allow it now. That's why it's best to find out their current rules. If I were you, I'd get your doula to tour CDH along with you, since she has never been there.
Original:
The first part of your question makes sense to ask here, but really and truly, do you expect people to be able to answer the second question? You need to ask the hospital! Perhaps your doula knows the answer if she works in your area hospitals. Especially if she has worked at CDH.
I did not have my babies at CDH, as I didn't live in Illinois at the time. But, I have had surgical proceedures there, and I was happy with their professionalism and their skills and doctors.
Good luck with the birth,
Dawn