OK, so if I understood correctly, you have at least 2 different separated email accounts.
The way I see it, the only relevant details for the main issue here are:
A_ Email account "A" is used "as usual", with SSL;
B_ Email account "B" is used with a specific dial up ISP phone number, and it doesn't use SSL.
So, what Pondus already suggested is the solution.
In your email client (assuming you use the same email client program for both email accounts), account "A" AND account "B" should be configured without SSL.
In Avast, email account "A" should be configured with SSL, and email account "B" should be configured without SSL.