If you lock her in a display stand or cage in the Summit, then you don't need to restrain her at all.
(Obviously doesn't fix the bug but solves your problem.)
If by "appear on the map later on" you just mean you're seeing duplicate characters/names, that can happen.
When you capture NPCs (Prisoners) or add them to your party (Guests), they'll appear in the Collection tab of the Items menu.
To get any use out of these characters, you need to unlock the Facilities tab. To do this, you need to get a "Point of Interest" which contains an Elevator. Elevators take you to the Summit. Going to the Summit for the first time unlocks the Facilities.
Facilities require Servants to run. Guests can be promoted to Servants. Prisoners can be promoted if their approval rating is positive. You can increase prisoners' approval by assigning them to the Cuddle Lounge Facility.
All the other Facility stuff is explained in that tab once you unlock it.
If you have a knife and are restrained in such a way that you can't properly hold a weapon, going near a crack causes you to put it in the crack, which allows cutting your restraints.
For example, I used a straitjacket on myself then went near a crack. When I highlighted the cutting option, it said "You use your feet to place the knife into a crack!"