Hi bergdoll,
As I understand it,you would like to redirect the Office 365 website to http:\\www.mysight.com\~subdirectory.
If so,you may need some 3-rd party solutions, such as HTTP redirection, to redirect the HTTP request from your Office 365 website at the current DNS hosting provider of the custom domain.Unfortunately,these solutions are beyond the scope of our support.
I would appreciate it if someone community member could provide a solution for this issue.
Thanks,
Keats Ge