Step 1) Display on a monitor the critical service-related and hosts so that a first support helpdesk services can intervene.
If i'm understanding correctly, you could do this via the "Problems" page:
Step 2) If the problem is not resolved within a set time, I would like to disappear (automatically) from view for the helpdesk first level of the critical signaling and show it instead to a second-level help desk.
Escalations are probably a good way to handle that:https://assets.nagios.com/downloads/nag ... tions.html
Though the "automated" part of it is much trickier. You might have to develop some sort of custom cron job to watch outstanding problems.
You might also look at multi-tenancy within Nagios Core. This is a pretty good presentation on the topic:https://www.youtube.com/watch?v=y3rOo0cHv5I