Change the split criteria to remove whitespace as well. Building on davorg's code:

my @sorted_list = 
     map { $_->[0] }
     sort { $a->[1] cmp $b->[1] or $a->[2] cmp $b->[2] }
     map { [ $_, (split /\t\s*/)[3,4] ] } @database_in;
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