Are you using the same logon credentials on the 2 affected teacher computers as on the other working teacher computers? Can you check that the time is synchronized on all computers properly? Besides this I recommend upgrading to the latest version (as of writing: 4.5.2) on both teacher and student computers.
Some technical background: first you should make sure the tray icon is visible on all computers. If it's not visible, the Veyon Service for some reason is not able to run it's own worker processes within the user session. The Veyon tray icon is provided by such a worker process. Launching the "Run program" or "Open website" features also launches a (different) worker process inside the user sessions as a helper process. This worker will then start the program or open the website and this way make sure the program or browser is opened with user privileges (instead of Admin/LocalSystem privileges which the Veyon Service is running with).
On computers where the tray icon is not visible, can you please check the VeyonServer.log file for messages starting with WindowsCoreFunctions and post them here?
Do you found the solution for this probleme, I have the same probleme, And I don't know how to fix it.
When I try to connect with user name to an other PC , he refuse informations entred and message appear : tentative d'ouverture de session en utilisant des informations d'identification explicites