$dbh, $timestamp and $server don't sound like variables that should be used from outside the package, so use vars isn't appropriate. They don't sound like they need to be package variables, so our isn't appropriate. my should be used here. (Actually, it would probably make a lot more sense for those to be attributes of any object.)

variables defined by “use vars” can end up being shared between the forked children ?

Variables aren't shared between processes. Each child gets a byte-for-byte copy.

I am occasionally having mangled data go into the database

It doesn't make sense for two processes to use the same database connection. Open a connection in each child.