The openHAB Cloud Server works pretty much exactly the same for OH 2.x and 3.x so what ever problem you experienced before is probably the root of any of your problems now. Using the cloud server and cloud connector is exactly as easy as it was in OH 2 as far as I know. You put in the user name and password for the myopenhab.org account under the remote settings in the app and you are done. There are no additional steps if you want to use BasicUI. There are some extra steps to make the Andorid App use MainUI instead of BasicUI by default but you are not looking for that.
There is an alternative way to authenticate with OH 3 but you would have had to change some settings to enable that. In MainUI follow openHAB API tokens | openHAB to generate an API token. You can then use that as the username without a password for local connections. But you are having problems with the remote connection and the API token doesn’t work with the cloud connector, just connecting to OH directly.
The only think I can imagine might cause a problem settings wise would be if you disabled the Implicit User Role in MainUI under Settings → API Security → Advanced. That would lock down the OH REST API to only work with authenticated users which would break BasicUI. But the default is to have that enabled and BasicUI should work when it’s enabled.
So ultimately all I could guess is that there is a problem with your specific phone (since it appears to work on your wife’s phone) and what ever that problem is is unrelated to the version of OH running.