Hi, I have no much knowledge about sendmail, mutt, etc. but I have a similar network as yours. Perhaps my experience helps.
1. Suppose you have a sendmail or postfix MTA running in your linux box. Send mail by yourself. This avoids rejection by the mail server of your ISP. 2. I run my own DNS and get my registrar having a DNS record to my dynamic IP. (The Cable connection can maintain that IP for long time if thay don't have a problem.) 3. Your DNS should have a MX (mail-exchange) record so that other mail server can drop mails to your domain. I hope this will simplify the problem. charlie
