1. A missing child shouldn't remove my constitutional rights. If that was the case we're literally ****ed because a child goes missing and you can thne be harassed by cops all you want who'll find something illegal (everyone owns something) and then put you behind bars.
2. I'd like to see your caselaw. Police are allowed to search properties in case of imminent danger such as hearing someone scream or seeing a fire or something along those lines, not cause a kid is missing, unless there's a case you have the disproves me.
I mean I'm sure the cop can make a case for exigent circumstances but that's a weak case at best.
They need a warrant to enter a car or house but not your backyard. You can ask them to leave but they are allowed to do that.