I don’t envy you given your situation.
For several technical reasons, AirTags are simply not well suited to finding “moving objects” …
… they were designed to locate stationary items left behind.
They are not “continuously updating” meaning they might tell you where a moving AirTag WAS … not where it IS.
Plus they depend on other iPhones being fairly close by. (The iPhone is actually reporting it’s own position as the “AirTag’s position”)
This article seems fairly well balanced and covers other important considerations:
https://conciergecareadvisors.com/air-tags/