Check for Updates does not show latest release

You got caught in the staged release of 5.15. What happens is that they roll out a limited number of copies of the new version (5.15) then stop and wait a while to make sure there are no major glitches. That's why you can't get 5.15 from your account or update it right now on the 2nd computer. Version 5.15 makes changes to the structure of the Quicken data file that 5.14 can't read. That's why 5.14 won't open a file that's already been opened in 5.15. However, all is not lost...

1. On your 1st computer, find Quicken.app in the top level Applications folder. It should be version 5.15.
2. Right click on this file and choose Compress "Quicken.app". This will create a file named Quicken.app.zip.
3. Move this file to the top level Applications folder on the 2nd computer using a thumb drive, Dropbox, or any other means of moving the file.
4. On the 2nd computer, double click Quicken.app.zip to uncompress it. You will now have 5.15 on the 2nd computer and this will open file that was backed up on the 1st computer.

Alternatively, wait a few days until 5.15 is in general release. I have not seen problem reports with 5.15, so I expect that it will be in general release very soon.