When I'm making a jacket
I always use interfacing on facings
Sometimes I top stitch the width of my foot in on the garment.
If I'm not top stitching I sew the facing and seam together right next to the seam stitching on the facing.
I always tack the facings down at shoulder and any other seams.

Since these are existing garments try tacking the facing at the shoulder. You can always try tacking a stiffer strip of interfacing to the facing. You could get some strings of decorative beads and do a design or put in buttons and buttonholes even if you prefer to leave it open and them undone.

No I don't think you should use any kind of glue--it would show too.

I think they ought to hang spammers....grrrrr.. okay, back to the subject!
I have had the same problem with facings. First, I check to see if I can catch the facing into a seam somewhere...I just hand tack it in place if there is something available.
Plan B is to take a piece of stitch witchery and cut it in half making it about 1/4" wide. I use about a 6" piece and apply it right at the edge of the facing which is generally about 2" in from the front seam and midway between neck and hem. I press it in place from the back, and using a fairly heavy press cloth between the iron and the fabric. So far it has worked very well, and I have been using plan B for about 30 years :^)
I have to wear dress clothes 6 days a week, so you can imagine that I have "stitch witched" a lot of facings! I also use this method on the back neck facings, if there is no center back seam. HTH