"Like it or not, Catholic hospitals cannot do things contrary to the Faith. People are aware of this. If they don't like it they should go elsewhere for their healthcare."
Multi-billion dollar businesses aren't organs of faith.  Ascension, Presence, etc. aren't little charity hospitals run by pious nuns.  That is the deal.  Catholic health systems are so large that they might be the only option that a person has.

"As for the rape: what I am saying is that as long as the drug given is contraceptive in nature and not abortion inducing, if the woman was pregnant it would not matter."
Emergency contraceptive prevents implantation.  That is one of the ways it prevents pregnancy.