A lot of these are speculative, but the main thing is that when they protected Naruto, they took critical injuries and likely were not going to live after that. Minato knew the only thing he could have done to properly seal the 9 tails fast enough was the Reaper death seal. The thing is, That will kill the user, as the reaper takes their soul when its released. Orochimaru survived the reaper, but he summoned it using a mask instead of the jutsu, and it still cost him his body. Minato on the other hand, can't do any such thing, so him surviving this encounter is out of the question.
As for Kushina, besides the fact that she was set to die without Kurama, she still dove in-front of his claw, and it pierced her torso in what is likely a fatal injury. Combining such an injury with her weakened body, and its probably next to impossible to save her life. At that point, Both Minato and Kushina are guaranteed going to die, or at least believe so. Sealing Kurama in either of them will probably still lead to their death.
As for why he only sealed Half of Kurama into Naruto, As per This answer, He couldn't seal all of Kurama into Naruto. Minato's Wiki entry notes that it was because Kurama was too powerful to be sealed into a newborn infant.
Edit 1: OP added some concerns in a comment, Responding here:
First, Any time Kurama was resealed in Kushina was filler, and as filler does not need to follow in faith of canon, they could do anything, including contradict the canon content. Second, Kushina even volunteered to have Kurama get resealed inside of her, to drag both of them to death.
While still weakened, Kushina used her diminished chakra to restrain the Nine-Tails. Despite fearing the trauma would kill her in her current state, Kushina volunteered to have the Nine-Tails sealed back into her body so that it would die with her.
So all in all, Kushina was effectively on deaths door, and had no hope on being saved. She had just spent 10 months pregnant, given birth, had Kurama extracted, and was left in that dying state for up to a few minutes with no medical help. As we found out later on, Naruto survived, but unlike Kushina, he was still healthy, young and strong, and had Sakura, second only to Tsunade in medical prowess, constantly healing him (and help from Hagoromo). So it actually makes sense that he had a solid chance of survival from the resealing. Kushina on the other hand, had several major events drain her power, not including loosing Kurama, so her being strong enough to survive was low at best.
In that respect, He probably could have sealed Kurama back into Kushina, but it most likely would have still left her dead and freed Kurama. A free Kurama would throw the tailed beast balance off, causing war, and Minato did not want to take such a risk when a safe option was available. That safe option, sealing half of kurama into naruto, also had one major benefit in Minatos eye, the fact that he believed Naruto could be the child of prophecy Jiraiya spoke about, and Naruto having access to Kurama's power would greatly help him succeed (that is also brought up in the answer I linked earlier).