Solving this sort of problem can be made much easier if you break it into parts. Use a simple regex to drop words containing doubled letters then you can use a simple regex to find repeated letters.

use warnings;
use strict;

my %words = map {$_ => 1} split ' ', "This will search for words with 
+doubled letters at positions";

print "$_\n" for grep {!/(\w)\1/ && /(\w).+\1/} sort keys %words;
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Prints:

doubled
positions
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