Calling all car people

unnamedAny suggestions on what to do with this?  It’s been pulled out a little bit since I owned the car, and a couple of weeks ago it got caught perfectly in a wind gust and pulled damn near completely off, although it’s still pretty nicely seated around the actual door handle so it’s not gonna detach anytime soon.

I have tried jamming the edges back underneath the lip with various sharp and/or thin implements, not limited to but including butter knives, sharper knives, putty knives, flat-head screwdrivers, and a few other things.  This works temporarily but looks like hell and sooner or later contact with my elbow works it out again.  I just tried to glue it back in place with some glue that was supposedly rated specifically for adhering leather (and, not for nothing, that I purchased at an auto shop) and I may as well have poured water or just pissed all over my car door for all the good it did.  There was literally no adhesion whatsoever from the glue, which makes me think that other kids of adhesive probably aren’t the right way to go either.  Unless they are.  In which case tell me about them.

Or just tell me to take the car to a detailer, assuming some sort of detailer is even the right kind of person to deal with this.  I don’t need an actual mechanic to take the door apart, do I?  Because that would be both expensive and insanely annoying.