G'day Steve,

Welcome to the monastery.

Here's a barebones example of how you can achieve what you describe:

#!/usr/bin/env perl

use strict;
use warnings;
use autodie;

while (<STDIN>) {
    print;
    /^B (\S+)/ && read_input($1);
}

sub read_input {
    my ($file) = @_;

    open my $fh, '<', $file;

    while (<$fh>) {
        print;
        /^B (\S+)/ && read_input($1);
    }

    close $fh;

    return;
}
[download]

Sample run (I added a 'pm_1081744_' prefix to your filenames; beyond this, the data is the same):

m
m
n
n
o
o
B pm_1081744_tst.bat
B pm_1081744_tst.bat
a
b
c
B pm_1081744_tst2.bat
z
y
x
w
1
2
3
p
p
q
q
r
r
[download]

So, I started wih the same STDIN input as you (m, n, o, B pm_1081744_tst.bat); the output is as you wanted it (abc from pm_1081744_tst.bat; then zyxw from pm_1081744_tst2.bat; then back to pm_1081744_tst.bat for the remaining 123); and, with all file data now read, reading again from STDIN (i.e. p, q, r).

I'll leave you to add custom input prompts and INFO messages.