Of course you could do this and other things provided that you are managing and in control of your website.Is there anyway to change our control panel to direct to our .com or correct this in a different way?
I think your problem may be that you bought a "package" deal where the web design company is providing everything, domain names and dns, site design, hosting, email, etc. As a result, you are totally dependent on that company and may not have the control that any website owner should have.
Do you have FTP access? If so, I recommend backing up your site(s) locally. Who owns the design? Could you change hosts and keep the design? Who owns the domain names? Could you change registrars if you wanted to? Could you keep your domain if you changed hosts? Could you use a different designer at your current host?