If the size does not matter, I suggest the following:
You create a partition on your USB hard drive slightly larger than the hard drive of your laptop. Then make a Disk to disk copy of your laptop HDD to that partition on the USB hard drive. Select Do not connect in the Drive letter for the selected partition on the Restore/Copy Parameters panel. The rest of the USB drive is at your disposal. And then start your computer from this disk. As you have R-Drive Image installed, it will appear in the programs on the startup disk. Then copy data back from the USB drive to your laptop drive. And again, select Do not connect in the Drive letter for the selected partition on the Restore/Copy Parameters panel.
The size of the USB drive should be larger than that of the laptop drive. The rest does not matter. When you start from the USB drive, letters C: and D: will be reserved to the disks on the USB drive, the disks on the laptop drive will have different names. But when you restart your laptop, the disks will have their original letters, C: and D:.
Well, I recommend to test that scheme first.