Manage local emails on two Mac computers
I would suggest using Gmail's powerful IMAP features to keep your emails synced on both computers. 

I have set this up for lots of people and it works great.

Get a Gmail account and go to settings - Accounts and Import.

You will have to set it up to check mail using POP3 and enter your mail server settings.  Next set up Send mail as choose Send mail from another address then put your outgoing smtp settings.

Next go to the Forwarding and POP/IMAP tab and enable IMAP and click on the Configuration instructions and it will give you the settings to enter into Apple Mail.

Once your Apple Mail is set up on both computers it will keep all your messages synced.  You can also set it up on your iphone or Android.