"provided conception has not yet taken place. Once conception takes place, what would be the point giving a women contraception? Wouldn't contraception be moot? Oh, right--you mean Catholic hospitals refuse to perform an abortion... And why does that bother you? "
How do they know that the women is pregnant if she comes to an ER after being raped?  Do they test her cervical mucus to make sure that she isn't ovulating?

" The hospital will not do a direct abortion, instead they will cut out the effected tube, saving the life of the mother, but nonetheless leading to the death of the child."
Which is less effective than giving a woman abortion drugs in some cases.

"Catholic hospitals will not script birth control--but women do not have to go to Catholic hospitals to get scripts for birth control now do they?"
If you read the story, you will know that the woman was never told they wouldn't do a ligation until she was in labor.  She had no choice because she wasn't informed.