Hi, I restore this quite old thread hoping to be of some help.
I found many threads, with many people complaining for this issue, but never found one with a working solution...
My case is pretty much the same: I'm using android Gmail app with another external account, and I was not able to delete any mail of this account from Gmail app, because after a short while it came back again.
So I checked the folder structure of my external account, via web site, and I found that the Trash folder was not very well defined: more specifically I had a second folder named Trash in the folder tree, probably created automatically by some email client I used in the past. This was not a problem for other clients, but apparently this IS for Gmail app.
I deleted this second Trash folder, and suddenly I became able to delete the email from the Gmail app!
Or better saying the deleted emails now go to the proper Trash folder as they should.
I don't know if this solution could work for anyone, but as said I didn't find any useful on the numerous thread created over the years... it worked for me. Good luck!
Regards.