Make sure you have the flexion on the rein you are tracking when coming down the longside. Prepare the horse by half halting, turn the shoulders first and keep the haunches behind the forehand on rail road tracks (haunches not swinging in or out). Ride straight on centerline, change the bend, then flexion then turn and keep the haunches straight behind, straighten onto the longside.
It is OK when beginning the exercise to ride straight down the centerline for more steps until he is truly straight, between the aids and then flexed in the new direction. Gradually shorten the distance on centerline. Other exercises to improve lateral flexibility are leg yield zig zags, serpentines, figures of 8s with simple lead changes (through trot or walk and as small as possible while keeping balance) and serpentines with gate changes (ie one trot loop, one canter loop, simple change through trot, one canter loop, one trot loop..).
They say money doesn't buy happiness -- well happiness doesn't buy horses!