Just noticed something on rewatch that makes me question the timeline
Lucy mentions the "great plague of 77" as the event that led to her mother dying. The show takes place in 2296, so a 19 year gap. Lucy has faint memories of her mother but not being in the wasteland, so we can presume she is maybe 4 or so in the flashback in the cornfield, so her character would presumably be in her early/mid 20s and Maximus is probably a similar age (maybe a bit older) as a result. However, she presumably is being told the quarantine/plague story and "recalling" that as a 2nd hand memory. The chalk board mentions the fall of Shady Sands was in 77.
New Vegas takes place in 81.
So logical conclusion
1) Hank quarantined people to avoid the general population knowing that his wife (or perhaps others) left the vault. It would also provide a cover to kill off people who knew too much. Hank was the overseer by this time. The computer entry mentions he was elected in 71, so we can presume he was in the vault before then. Since the plague is a "historical event" in the vault, other older people would remember this and support the plague story
2) Since this date would be supported by other vault dwellers, that means that Rose would have left the Vault in 2077 with the kids. While we don't know how long this "plague" story lasted, the fact Shady Sands falls in 2077 is too much of a coincidence when taken into consideration with the plague cover story.
3) Lucy's young age in Shady Sands would explain why she doesn't have clear memories. However, she doesn't remember being taken away from her mother, or a nuke, or anything like that. So unless you're dealing with some type of traumatic repressed memory stuff, we can presume her removal from Shady Sands wasn't traumatic. In the later scenario, Hank showing up and secretly taking the kids could make the most sense.
4) We can assume that Hank nuked the town (or arranged for it) once he and the kids were safely away. The fact that Rose was a feral ghoul means she was probably pretty close to the blast, which means that she was still in the city or extremely close to it at the time of the nuke, which means she either had not noticed the kids were taken or at the very least she had not had a chance to pursue Hank for whatever reason
5) Therefore, we can conclude that Shady Sands was nuked in 2077 or maybe 2078 at the latest, which fucks with the New Vegas timeline