I don't recall hyperspace ever killing people in an Asimov story.
The only story in I, Robot in which the discovery of the hyperspace drive is prominent is Escape!. However, hyperspace doesn't actually kill anyone. Technically, both the characters experiencing the hyperspace jump, and the people monitoring them, consider the travelers dead while in hyperspace; however the travelers keep thinking, talking, and so on, so it's not clear to me why we should consider them dead.
The positronic brain in charge of building the drive also considers the travelers to be dead during the jump. This is a violation of the letter of the first law of robotics — though not of the spirit, since nothing irreversible is happening to the humans. The story revolves around the positronic brain's reaction to this borderline violation of the first law.
As for “one AI could not construct the ship while the other could”, USR's competitor's supercomputer didn't understand the subtlety and completely broke down from being strongly ordered to violate the first law. Susan Calvin handled USR's supercomputer better, so that it only played pranks, distanciating itself from what it was doing, but survived the hurdle.