You need to keep track of previously viewed rows. Assuming the data is sorted by sequence id,

my $last_seq;

while (<>) {
    my ($seq, $p1, $p2) = (split)[0, 2, 3];
    ($p2, $p1) = ($p1, $p2) if $p2 < $p1;

    if (defined($last_seq)) {
        if ($seq eq $last_seq) {
            print(",");
        } else {
            print("\n$seq ");
        }
    }

    print("$p1..$p2");

    $last_seq = $seq;
}

print("\n") if defined($last_seq);
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Update: More like your code and less like your explanation:

sub extractseq {
    my ($seq, $ranges) = @_;

    system(extractseq =>
        "-sequence=$seq.seq",
        "-auto",
        "-stdout",
        "-separate",
        "-reg=" . join(',', map { "$_->[0]..$_->[1]" } @$ranges),
    )
        and die("system: $?/$!\n");
}


my $last_seq;
my @ranges;

while (<>) {
    my ($seq, $p1, $p2) = (split)[0, 2, 3];
    ($p2, $p1) = ($p1, $p2) if $p2 < $p1;

    if (defined($last_seq) && $seq ne $last_seq) {
        extractseq($last_seq, \@ranges);
        @ranges = ();
    }

    $last_seq = $seq;
    push @ranges, [ $p1, $p2 ];
}

extractseq($last_seq, \@ranges) if defined($last_seq);
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Update: Finally, if the input isn't sorted or if you prefer something simpler (at the cost of using more memory),

my %ranges_by_seq;

while (<>) {
    my ($seq, $p1, $p2) = (split)[0, 2, 3];
    ($p2, $p1) = ($p1, $p2) if $p2 < $p1;
    push @{ $ranges_by_seq{$seq} }, [ $p1, $p2 ];
}

for my $seq (keys(%ranges_by_seq)) {
    my $ranges = $ranges_by_seq{$seq};

    system(extractseq =>
        "-sequence=$seq.seq",
        "-auto",
        "-stdout",
        "-separate",
        "-reg=" . join(',', map { "$_->[0]..$_->[1]" } @$ranges),
    )
        and die("system: $?/$!\n");
}
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