The Net::SMTP documentation says that won't work. Standard Perl lists (I think it can also take an array reference) are what is used for multiple addresses. to is a synonym for recipient so there isn't any need for using both or making multiple calls.

$smtp->receipient($MailFrom1, $MailFrom2);
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Also, what is up with:

my $MailFrom = 'postmaster\@testme.com';
my $MailTo1 = testmeuser@home.com};
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Did the code get mangled from posting because I don't think that will compile. In any case, the second string should be in single quotes. You don't need or wan't a backslash inside single quotes.

my $MailFrom = 'postmaster@testme.com';
my $MailTo1 = 'testmeuser@home.com';
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Finally, should be checking the return codes of the calls. You don't know if the recipient call is failing because the mail server is rejecting the address or because the addresses are misformed.