I created a new user role from a duplication of the Editor Role called "Message Manager". This role has the ability to post/edit/delete all pages and posts/cpt just like an editor can.
When they go to post a new post/cpt they get an error "Cheatin’ uh? Sorry, you are not allowed to access this site." But the post/cpt still gets posted.
Also the "Move to Trash" link on all pages/posts/cpt is now missing when logged into her account. I still see the links logged into my admin account.
Based on this I was able to confirm that the settings are indeed correct for your user role to be able to delete the posts. Perhaps there might be a plugin conflict.
The next step is that I would recommend that you temporarily disable all your non-toolset plugins and check again. If there are no improvements would you mind allowing me to have admin access to the site so that I can do some further checks ?
Yes, you can use the duplicator plugin to make a copy of the site. I went ahead and deleted all user accounts other than mine, yours, angelica's (the original account with the issue) and your test account for security reasons so it should be good to clone.
