You can't really have it both ways - you can't say they should have been told that there license was conditional on providing care contrary to their religious beliefs and at the same time say that no other alternatives were available in the community. If you ask me, and I'm sure you wouldn't, I'd say the community is damn lucky the Catholic Church decided to provide hospital services in a community where the state and/or a for-profit private entity refused to set up shop. In addition, I'll venture that the Catholic Church set up shop there because there is a large Catholic population in the community.
As for providing all medical care possible to all possible patients, that's a pretty high bar to set for any institution, public or private. You make the mistake of equating a constitutional right not to be barred from accessing abortion services with a constitutional right to be provided with abortion services in any and all medical facilities a person may enter. The Catholic hospital is not denying the woman the right to an abortion, just not in their facility.
As for the hospital taking "our tax dollars", I haven't seen any proof that the hospital receives grants or other money from the community or state simply for existing - they no doubt receive payment from the state for serving medicaid and medicare patients, but surely you don't suggest that no facility that doesn't provide abortion services can receive payment for any service funded by the government programs, or are you? Is your position only related to abortions? How about if a facility doesn't have MRI equipment - are they banned from receiving government program funding for other services provided? Again, it is not the Catholic hospital's fault that there is no abortion or public facility in the community and they are not responsible for providing all services possible, just to provide adequate and safe services as government by medical licensing agencies. And besides, most Catholics and most pro-life people also pay taxes and I'm sure they're pretty satisfied for the most part with the services they have in the community.
As for saving a woman's life - the woman didn't die did she? Is she suing from the grave or her family suing because of her loss? No. So, the woman was pregnant and something went wrong - she went to the hospital and was given treatment to help her save her baby - presumably, that's what she wanted or she wouldn't have left the hospital the first two times. When it became apparent the child couldn't be saved, the mother was treated and her life protected. The hospital is being blamed, apparently, for doing everything they thought they could and should to try to save the life of the child.
Perhaps, as Obama would like to do, you'd like to see Catholic charities get out of providing such services and hospitals and leave it to secular private profit entities or public government facilities. Clearly, from what we know so far, no such private or public government facility took up the task of providing this community with the services they need, according to you. Perhaps it would be better for the hospital simply to shut down, leave the 40,000 or so residents without any hospital, all so some women can get abortions on demand.