One way to solve this is to put a low cost Linux computer next to the remote device, with its own ethernet support. You log into the computer via SSH with X-forwarding, and then run the IDE on the remote computer with the display on your computer. I think I read that some people have compiled the Arduino IDE so it works on the Raspberry Pi, but it is fairly slow (on the other hand, the R-PI doesn't have much in terms of footprint, and it can run headless without a monitor).
Or you can use one of the various VNC versions, and run the graphics through vncserver, and connect to it via vncviewer. I'm at work right now, but I have a work at home laptop that connects on the corporate VPN system, and from my laptop at work, I can connect to the VNC server on the remote system, and run whatever graphics program I want. Note, I don't get sound, but that is usually not an issue.
For that matter, I got a Kindle Fire for Christmas, and it can support both VNC and SSH, and I have tried out the local systems in the house. If I was going to use a tablet for remote graphics all of the time, I would want to get one that supports a bluetooth keyword, which the Kindle Fire does not (Kindle Fire HD does support bluetooth I think).
Under Windows, you could use VNC (which was painful when I used it years ago), or I think Remote Desktop. Since I rarely use Windows, it isn't an issue for me.
Obviously the further away you are from the system, the more network latency becomes an issue. But in the past, when my local network was down, and I needed to get something done for work, I have used a modem (remember those?) and dialed into the California office from Massachusetts and setup networking and did remote graphics (slowly) that way.
If the speed of your connection would make graphics an issue, you could go through the steps to build Arduino objects outside of the IDE, and then ship the .hex file to a remote computer, and then log on with ssh and use avrdude directly. If you aren't comfortable with make, command lines, etc. it can be a long learning curve to get up to speed.