Are you trying to perform the acknowledgement from another domain within your organization or from outside it entirely? If it is another domain within your organization it is possible to create a trust between the two domains, however if it is outside your organization entirely then I think you would need to have a VPN in place...
Yes it will be outside the organisation.
Which version of PI Notifications are you running?
If you are running the legacy Notifications (2012 and older), the acknowledgement web page is installed on a web site. If the web site is publicly exposed it should work fine. Another possibility, as mentioned by Donal Wylde would be to use a VPN to access your internal network.
If you are running the newer Notifications (2016 R2), the acknowledgment is done on Event Frames. This can be done through PI Vision. PI Vision is an IIS web based application. If the web site is public facing it should work, otherwise you could use a VPN to access the internal network.
Hope this helps,