The easy way to solve this is to just log on directly to the remote server using Remote Desktop and use Management Studio on that session, but this is not really desirable for several reasons: not only will your Remote Desktop session consume quite a bit of memory and server resources, but you’ll also lose all the customizations and scripts that you may have handy in your local SSMS configuration.
Your mileage may vary with these solutions, and I don’t have the requisite skills to elaborate on the finer points with regards to when one solution will work over another, so just give them a try and see what works for you.
I prefer Daniel’s second option, using runas.exe.