Quoted from radium:Not construction adhesive, just good quality wood glue and clamp. If it’s still bad you could add some corner blocking on the inside.
In order of easy to more involved: 1) Spread the pieces apart and good wood glue in the seam and then clamp it up. 2) Same as 1, but cut wooden blocks and glue those along the inside seam as well to give the glue more surface area to secure the pieces. 3) same as 2) except counter sink screws from the exterior instead of clamping (but still use glue!). Follow this up with wood filler and then paint to match.