It sounds like you've got a rather convoluted setup; often when things seem difficult in Perl, it's a sign that you may need to rethink how you're structuring your code. In this case, your modules.

However, you did ask, so--this seems to work. I've only done B.pm, not C.pm, because they should be quite similar if I understand what you're asking.

Here's A.pm (your $i_am_the_problem is now called $problem):

    package A;
    use strict;
    use vars qw/@EXPORT @ISA $problem/;

    use Exporter;
    @ISA = qw/Exporter/;
    @EXPORT = qw/$problem/;

    1;
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Here's B.pm:

    package B;
    use strict;
    use vars qw/@ISA @EXPORT/;

    use A;
    use Exporter;
    @ISA = qw/Exporter/;
    @EXPORT = qw/foo/;

    sub foo { print "problem is $problem\n" }

    1;
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And here's a small script that sets $problem, then calls the exported function foo:

    use A;
    use B;

    $problem = "bar";
    foo();
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That said, again: you really may want to rethink your code design.