The following will work. There was another problem with your example. "(Jack) and (John)" the literal string, does not match itself as a pattern with capturing parentheses.

my $new_value='$2 and $1';
my $string="(Jack) and (John)";
my $regex=qr/$string/;
$string = "Jack and John";
eval "\$string=~s/\$regex/$new_value/";
print $@ if $@;
print "$string\n";
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