my $from = "my (mom)";  # UPDATE: was '"my (mom")'
my $to = "our \$1";
$content =~ s/$from/qq{qq{$to}}/ee;

##</code><code>##

use DynScalar;
my $from = "my (mom)";
my $to = dynamic { "our $1" };
$content =~ s/$from/$to/;