Do visit Moutside as often as you can. Yet also give KitKat equal time. I liked to use lots of treat rewards for both. When I would visit Marvin, I would always bring a few treats to offer when I first arrived. I would save a few to give when I left. I then would give my resident kitty a few extra treats and play time too.
As for room swapping time, you want to start slowly. Also be sure that you can handle ( pick up) Moutside so that if you sense fear or need to quickly get her back to her room, you can do so. I liked to start with just another room and not my entire house. That is too overwhelming. I used to take Marvin to my bedroom and then I allowed him out into the hallway. It took weeks before I allowed him to go downstairs. I liked to start with just 5-10 minutes at first. Always rewarding and offering treats. Then back to the safe room and more treats. You can do this more than once a day if all goes well. If Moutside is afraid and doesn't want to leave the room, just leave the door open for a bit. It sometimes takes them awhile to want out. Yet do be sure you can safely get her back to her room.
As for room swapping time, you want to start slowly. Also be sure that you can handle ( pick up) Moutside so that if you sense fear or need to quickly get her back to her room, you can do so. I liked to start with just another room and not my entire house. That is too overwhelming. I used to take Marvin to my bedroom and then I allowed him out into the hallway. It took weeks before I allowed him to go downstairs. I liked to start with just 5-10 minutes at first. Always rewarding and offering treats. Then back to the safe room and more treats. You can do this more than once a day if all goes well. If Moutside is afraid and doesn't want to leave the room, just leave the door open for a bit. It sometimes takes them awhile to want out. Yet do be sure you can safely get her back to her room.