Gate passes are issued at US airports where TSA (or a contractor) provides the security checkpoint. While it is the carrier which physically issues the pass (it looks like a BP), it is pursuant to TSA rules.

As a general matter, gate passes are easy to come by with close to any form of a decent reason. But, if OP's child is traveling under any form of a UM program, it is that program's rules which will dictate how the process works.