I have used hot hide glue for this.Always worked for me,never yet had a failure.
When you separate the pieces ,just use a heat gun on the seam.The glue becomes liquid again and the pieces slide apart.Another advantage is no clamps are required to glue up.
Although I usually clamp the work til the glue solidifies.This usually takes 10 minutes or less,then you are ready to machine.
As far as the hot hide glue in a bottle that does not use any heat to make the glue,I have never used it,just used the hot hide glue granules or flakes.I heat the glue in a weighted glass jar that sits in a crockpot filled with water.The reason for the weight is too keep the jar from floating .The glass jar means no clean up when done. The crockpot stays clean,got one at a yard sale for $5.00.
mike