I well understand how you feel OP. It's highly unfortunate that you more or less had to prove to a stranger in uniform with a gun that you were, in fact, a decent parent, and that you had to do so in front of your children and wife.
I wish the person who called the cops had exercised better judgement (assuming your side of the story is 100% correct). I hope they believed they were doing the right thing.
The law is blunt instrument. It should be a last resort, not a first one.
It sucks that you became "collateral damage" in this affair. If I were you, I would calmly and patiently ask other adult members who were at the pool until I found out who had called. You can BET whoever was moved to call probably revealed themselves with a loud comment or two before doing so.
Then, I would take four hundred and twenty-seven very deep breaths, followed by a series of cold showers.
Then, I would attempt to constructively and non-confrontationally engage that person in a conversation about this incident.
Who knows? They might not be a complete asshole after all. They may simply have been wrong.