You’re just not giving us enough info to help you out.
My immediate suggestion as im reading the post would be to extend a vent straight up through the roof of the garage, but then you claim there is no easy way to vent outside.
Without sketches of the layout of the house and/or photos I’m not sure how we can help. Is there a window in the laundry room? Can you set up a flexible vent that goes out there?