For a short coat or a jacket your wife/girlfriend/date/play partner can lower her arm to the side and back, as if she were starting to pose for having her arms tied behind, or having a binding arm sleeve applied. But more seriously... hold the coat as in step 3 and slide the arm hole over her hand and guide the sleeve up until her arm is fully covered. Repeat for the other arm.
Smooth the coat on her shoulders. A few smoothing strokes down her back also helps. Even if the coat is already smooth at the back... smooth it anyway, especially at the small of her back. She will appreciate it. You are likely in a public place so stop the smoothing at the small of her back. No need to smooth, slap, or caress her incredible, delectable ass just yet. "Smoothing" her front is also a 'no-no' in public.
While you are behind her you can whisper: "I love you!", or "I want you", or "Thank you, I had a lovely time" or "I want to tie you up in the dungeon in that 'hands up' pose you just did, spank your ass black and blue, then fuck your brains out". Whatever you say, keep it low. You're in public. Whispers are more powerful when only
she
hears it.
You may be aroused at this point. As you may be standing quite close behind her, she may be aware of your erection (or in-progress erection). No nudging or grinding motions, please. (That can wait until you get home--or to the car, at least). The line separating chivalrous gentleman from 'pig' is rather thin at this point. Do not cross that line. (If you get your kicks having sex while wearing a pig snout... not a problem... but again, wait until you get home.)
If the coat or jacket is luscious leather or rubber, and that's your kink, do not drool or grope/fondle the coat with or without her in it. You can lick/grope/fondle her and the coat when you get home.
You can use the above BASIC directions if, say, on a lunch with your mother or aunt. You should know instinctively which of the extra steps to leave out--or you're beyond my help.