Before you press APP, are flying the runway course? It seems you are not, because you mention the diamond turne and passes the course.
I say this because if you are slightly off, just a few degrees, when you press APP it will correct and align fine.
But if your heading is too far away from runway course, and the plane needs a steep turn to take it on course, there is no time for it to recover and a pendul movement starts without never aligning.
Another thing, are you above glide slope? Try to position yourself like 4000ft at 20 miles, that will give plenty of time for the autopilot to adapt corrections.
Anything I say is...not as serious as you think