The HST is nearly twice as high as the ISS, so it is either one or the other. There is no way to lift a shuttle from the ISS to the HST anyways, what would be the point? It is easier to go all at once, or just don't go at all.
Tom, I believe you refer to the Centaur upper stage rocket. In the beginnings of the shuttle program, it was decided to use the shuttle as a carrier for launching deep space missions (ie, Galileo) and DoD missions by raising the rocket in the payload bay before liftoff. There was a huge amount of debate about the dangers of such a mission, it is just not a good idea to have cryogenic propellents in the shuttle's payload bay.
Discovery and Challenger were modified to carry the Centaur, and they were ready to begin launching at the time the Challenger was lost. They would have flown out of Vandenburg for polar orbit missions. That is another problem, in order to reach polar orbit, the shuttle has to launch from Cali, and fly over land. So it something goes wrong, we get what happened over Texas in February 2003.
When Challenger went down, the DoD pulled out of the project, the Centaur was scrapped, as was the nearly complete shuttle facility at Vandenburg. It took nearly two years to launch Galileo, and they used the lower powered upper stage type launcher from Atlantis on STS-34...