Hi Frank,
You might be overthinking the problem a little. It's likely that you could find an RDP to get access to your laptop, but since you're using UPC you're unlikely to have a static IP address (which would be needed for RDP), which means you need to use an online service which allows you get access to your UPC router. Then you'll have to configure your router to redirect you to your laptop for RDP requests.
Now the good news: You can set up Outlook to leave an email message on the server for a certain period (say 14 days), then set up your phone to also receive the emails (this needs to be configured to never delete messages for the server). Using this scheme you'll always have a copy of the mail on Outlook, and will also have access on your phone...