Welcome to SolidWorks forums Rob.
From your point it's quite possible that you might be trying to access a dual monitor thru single monitor and SolidWorks window is appearing on the other screen. If this is the case then you need to set up the option to access the dual monitors (can't find right now which option but there is one check box in the display settings).
You might also find this post helpful for your future reference
I am able to run SW fine using Remote Desk Top o my machine. However, Some of my menus open on my secondary screen and not the primary. The remote machine only had one screen so some of the menus never appeared but the machine hangs. My solution is to have 2 screens on the remote machine, or to change my settings to one screen on my work station if I know I am going to need to remote.
It is possible *
It severely depends on your network. I can remote in and open SW but can't be truly functional due to network limits on bandwidth set by IT.
Can you suffice with eDrawings for your remote work? Or if it's a network license just remote in to get the license but run SW on your local machine.
I often run SolidWorks via remote desk top when I am traveling and have only a lame notebook to work with. I've never had any issues other than being slow and having too small a screen. I run a single monitor, so I'm guaranteed not to have the problems others suggest that multiple monitors can cause.