should the federal government install Armed UnderCover Officers at all schools in the united states?
No, the federal government shouldn't install armed officers at schools.
School districts might want to hire armed officers, or schools could be treated like the bad walmarts where they have a police substation inside or next door.
I'd say get the insurance companies involved.
Maybe have the federal government demand insurance companies offer "mass shooter" insurance or something to schools.
If a "mass shooting" occurs on the premises the family of each person killed gets a payout of 10 million or something.
Then the federal government can ACA the schools forcing them to buy insurance or have their funding withheld.
Expect all sorts of action taken to secure schools and children once you threaten the money.