Well with most things I'm sure there is more to this than meets the eye.
That said, I'm making a couple of assumptions when I say to hide the gun and keep quiet.
I'm assuming dad knows he has it, and since dad hasn't asked for it back that certainly sounds like implied permission, he just doesn't want grandma to know for whatever reason.
Grandma may run the household, but she's not the legal guardian I'm assuming.
Now, if dad does NOT know he has it that's a whole other can of worms and there's probably a law or 2 being broken and the best thing to do is pony up.
But, it sounds like Dad at one time or another gave permission for all this to happen, but now he's trying to placate grandma.
The Bersa, for both The_Sheriff and his dad, appears to be one of those "out of grandmas sight, out of grandmas mind" things.
If that's not the case then no, don't hide it.
But, if dad gave him the Bersa but hasn't asked for it back specifically, that says a lot in my opinion.
Sheriff just needs to be really careful here, one wrong move could impact his ability to own firearms for the rest of his life, as well as other things.