How do I access a mobile mailserver on a mac as opposed to a web mailserver?
Via The Browser
You'd have to send a mobile user agent to the mobile.company.com (there's a redirect on desktop devices). Safari will get you there via User Agent in the developer tools. First turn on Developer Tools.

Then change the user agent.

Now you should be able to access mobile mail server as a mobile user: mobile.company.com. I'm not sure if your ISP provides a webmail interface for mobile users. If not, you won't see much there.
Potential Solution: Spoof User Agent in Desktop Email Client
I can't quickly find an email client which directly spoofs user agent. If I had to guess which ones might be capable of offering an alternative user agent, you could try either MailMate (powerful high configurable shareware) or Thunderbird (geeky open source with an option for everything).
Contact info to MailMate creator Benny Kjær Nielsen is here.
Alternative Solution: Clean Up Your Mac's Certification Authorities
You may find it easier to reset your security certificates. Make sure Keychain Access is set up this way.

You should also delete expired or invalid certificates from under the System sidebar menu. Once you've done both of these things, you should run Software Update as Apple should replace some of the now missing certificates. Certificates and Signing Authorities can be imported by hand but that's beyond the scope of this answer.
I've just done this myself and it's allowed Chromium to load Github again. It may work with your email security issues as well. This is the lasting and flexible solution but perhaps the hardest to pin down.