Can I put an associative array within another associative array without all the data in them getting jumbled up?

Yes. That is a Hash of Hashes, HoH in short. see perlref and perlreftut. In fact you can create any kind of data-structure using perl-hashes and arrays. I donīt know if there is a "deepness"-limit but i doubt that.

#sample set up a hash of hashes
my %h =
(
    key1 => { subkey11 => subval11, subkey21 => subval21 },
    key2 => { subkey12 => subval12, subkey22 => subval22 },
);

#access it
print $h{key1}->{subkey11};

#loop it
for ( keys %{$hash->{key2}} )
{
    print $hash->{key2}->{$_};
}
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Update:
And yes, show us your code. But be sure to strip all non-relevant parts.