I have come up with some headcanons for the bad future timeline:
After Lucina's parents' death, Frederick became a father figure of sorts for her (and her sibling, if she has one).
On the topic of her parents' death, Frederick doesn't tell her about Robin being the one to kill him, because she's so young at the time that he doesn't think she could handle it. He intends to tell her when she's older... but dies before he can get around to it. As such, she only hears about Robin killing Chrom through rumors.
As Chrom's eldest (and possibly only) child, Lucina becomes exalt at a young age, but Lissa is her regent until she becomes an adult.
Grima's first action after killing Chrom was to kill Validar, since he had outlived his usefulness to it. They were the first two Risen that Grima created after its revival.
Most of the Shepherds managed to escape the Dragon's Table. At the very least, Owain, Gerome, and Noire's parents manage to escape. Nah's parents, however, do not.
