DNS records: Remote A record for website and local server for mail server
Solution 1:
You need to set up a new DNS entry, since right now since mail/web are shared on Server1. After that's complete, set the MX to the mail host & update the top-level to point to Server2.
Something like this:
example.com. IN A 10.0.0.101
mail.example.com. IN A 10.0.0.100
example.com. IN MX 0 mail.example.com.