Trashed email reappears

Uggggh.....Apple and Google mail. The last update allowed me to return to Apple mail which I had left because it would not sync with my Gmail account. I was so tickled that they appeared to resolve the problem, then in about two weeks. I still am able to retrieve my email, but when I select emails to delete (or archive) they disappear from my inbox only to return if I select another folder and then return to my inbox they are all there again. My inbox just swells with all these read and archived messages. The only way I have been able to eliminate them from my inbox is to use my iOS devices to delete my emails. Whats up with that? My Gmail settings in mail are set for IMAP communication. What else can I check? Is anybody else having this issue?