To get the full path to the script you're currently executing, you can use either of the following chunks of code from PerlMonks. File::Basename:
#!/usr/bin/perl -w
use strict;
use File::Spec::Functions qw(rel2abs);
use File::Basename;
print dirname(rel2abs($0));
or CWD can be used for this purpose. CWD example:
use Cwd;
my $dir = getcwd;
It should be possible to build up a full path using the base directory, plus your knowledge of the relative placement of the initial script and the second script you'd like to invoke. That way, while you will be using an absolute path to invoke the second script, you're only hardcoding a relative path?