You can get a "sweep" for the bottom of the door at the local Home Depot or Lowes. Sounds like a wall with insulation would help in the furnace room, as well as a solid door on HER side. The louvered door would need to remain for fresh air for the furnace. (I assume it's gas??) A solid door will also help. You might consider an insulated metal door, complete with threshold. The brick mold on the outside could be replaced with regular casing. Sound transmission is a hard to deal with.
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