So much going here.
A few questions:
Did you send both to live at Sunshine, and/or did you assign each separately to the city planner's desk to be the leader the leader of Sanctuary?
When you look at click on the Blueprints of CP desk and get the city details, who does it say is leading Sunshine?
Is your problem that Curie and Connie aren't in Sunshine when you expect that they should be or that even when assigned as a leader they don't show up in Sunshine?
There is a known vanilla bug with Curie:
https://fallout.fandom.com/wiki/Curie
"Upon dismissal Curie will reappear outside the medical room in Vault 81, regardless of where she is dismissed, even if dismissed to Sanctuary while in Sanctuary, she will immediately sprint toward Vault 81. [verified]
- Workaround: Reload an earlier save file and don't give the cure to Dr. Forsythe at the end of the "Hole in the Wall" quest until after speaking to Curie inside the doctor's clinic. She won't actually enter the room herself, so the player character has to get behind Curie and push her into the clinic. She will then initiate the proper dialogue to become a companion and will stay at the player character's chosen settlement. Alternatively, resetquest comcurie followed by setstage comcurie 83 will trigger the join companion dialogue, after which Curie can be moved as required."
If Curie will not remain in Sunshine, you might check to see if you've caught this bug.
(I'll add that you may also try making Curie the leader via the blueprint options on the CP desk. I mean make her the leader with the desk options and not via assigning her to the desk in workshop mode. Doing this with Codsworth will get him to move from his spot in Sanctuary even when his quest stage would have him camping out. It may work similarly for Curie.)
Since Connie is only available to be a leader through an add-on, and not with SS/RotC itself, what add-on are you using? Which ever it is, you might check it's nexus page to see if anything weird is getting reported about Connie.
You can't normally move any of the Abernathy's to other settlements, the only way to get them to move is by assigning them as a leader via the CP desk. This thread may offer some insight/help with figuring out what's going on with Connie:
https://simsettlements.com/site/index.php?threads/connie-abernathy-wont-go-home.6891/
Like I said above, there's a lot going on to figure out. I'm not sure I'd be comfortable jumping to this conclusion just yet.