Yes, there are 2 doors, like in a hotel. Both can be locked or left open, whichever you choose.
It's no different than having a wall there, so doesn't take up any extra space. I think the sofa/love seat is just situated against a different wall if you had a cabin that didn't connetc. The one time we booked late and could only get a room with a connecting door, we heard nothing form out neighbours.
Did you get your Mother the connecting room or are the 3 of you going to share?
Have a wonderful trip - you'll love this cruise and Hawaii is so beautiful.