I have seen that the URL that is sent in the email notification for filling/submitting the survey will domain name that the admin user used to access and sent invitation.
So if I logged in to the survey tool admin module using localhost and then invite someone then the invitation mail will have URL like https://localhost/limesurvey/index.php/survey...
If I logged in to survey tool admin module using domain name (example.com) and then invite someone then the invitaiton amil will have URL like
example.com/limesurvey/index.php/survey
...
If we have 2 installation pointing to same database and one of the installation's admin module is deleted and we use the installation that is having admin module, now from that installation we have to invite users for survey, ultimately the initiation mails will have the domain name of the installation which is having admin module.
I think the solution to have 2 installations can help me if we have a feature to specify what should be domain name of survey in invitation mail. But my understanding is this feature is not available as of now. Can you please let me know if I can change the domain name in invitation mails without changing any of the php code.