Update/Edit My Summary Tab

We are running into a SERIOUS problem where our technicians are missing Requests. We assign the requests to their group with the intent someone in their group will take ownership of the request by "Pick up" but they are not. So, I am looking at various ways I can resolve this problem. The best way I can think is changing the My Summary view and including requests that have been assigned to the technician's group as well as directly to the Technician. Is this possible? Can I modify the My Summary tab?

Another alternative is to automatically resend a notification to the Group if the ticket has not been picked up after a certain amount of time has passed. Can this be done?

Thanks for your help.