Can I make the Base URL for Back Office different from front Office pages?

[PrestaNoob852]

I am in the process of designing a new store. The owner doesn't need to have an SSL cert because he is using Paypal for all customer interaction securly. However, I want to use SSL for the Back Office. So I am using the Shared SSL certificate that his host offers. I went into Preferences -> SEO & URL's -> Set Shop URL. I put the normal site name into Shop Domain, I put the shared server name into SSL Domain, and in Base URL I put in the account name which is required in order for the shared SSL to work properly. So the SSL domain is now something like this:

 

SharedServerName.com/~AccountName/index.php

 

Then I was able to log into the Back Office just fine using the shared SSL cert.

 

The Problem comes into play when I go to the real domain address (not the shared server name). The site is working just fine, but it now has the account name listed there too. So the customers would see something like this:

 

RealDomain.com/~AccountName/index.php

 

Instead of:

 

RealDomain.com/index.php (which is how it should look).

 

The Question would be if there any way to make the system use one Base URL when going to the actual Store that the customers see and one Base URL for the Back Office only?

Edited April 7, 2015 by PrestaNoob852 (see edit history)