Liquid Nails and other construction adhesives are very hard to remove, so much so that cutting them off is the effective method.
To remove two wood pieces or other construction materials, I suggest you use Windshield Cut-Out Wire (also called music wire), available at most automotive parts stores and cut a length of wire about two or three feet longer than the width of the part to be removed.
Starting at one corner of the two pieces, work the middle of the wire under the edge of the part. Connect simple wood handles to the ends of the wire by wrapping the wire around some wood dowels or sticks. Be sure to wear heavy safety gloves to protect your hands from this cutting wire.
Saw back and forth with the wire, using moderate pressure as you pull on each end of the wire. After a few inches have been cut, use two screwdrivers to prop open the gap now cut between the two pieces of material. Prop these screw drivers in the gap to prevent the adhesive from re-sticking, which can happen from the friction heat caused by the wire abrasion.
Continue sawing and moving the screwdrivers as you go until the part is loose and can be removed. Scrape away any residual adhesive with a sharp chisel or tool. If the adhesive is too hard to scrape, apply a light layer of baby oil. NOTE: Do not use baby oil or any other softening material if you will be painting the surface. The oil can stain and contaminate some types of paint.