First, I’m happy that the twitter service has helped you and those you care about. Those are all very good use cases and we can all see why Jack Dorsey would state that twitter would drive to be a daily utility.
But that is the thing, something like that should be a utility that our phones should be able to tap into. For example, I live in California and we have something called an Amber Alert. You get alerts without the need for an account. You can get alerts on your phone, billboards and radio.
As a society, we should be making sure that services such as this are expanded to handle use cases as you have described them.
Now, as far as the question of how to use the twitter app to get you what you want. I don’t know if they have a “vip” notification group on the roadmap. I would hope that they discover it needs to be there since they wrote:
We’re committed to understanding why people hire 3rd party clients over our own apps.
link: Twitter company email addresses why it's #BreakingMyTwitter | TechCrunch
Good discussion.