Obviously Melodyne is correctly activated on your iLok (otherwise you wouldn't be able to use Melodyne at home either). The problem must lie with the computer in the other studio. Check the following points:-

The same version of Melodyne (uno, plugin, cre8 or studio) must be installed on both computers.

On the computer in the other studio, you must enter a valid serial number and select iLok in the field marked Method.

Note: If you aren't sure whether the studio you are due to visit has a licensed version of Melodyne, write down your serial number and take this as well as your installation CD to the studio with you.