There are many ways to do that. I have used XXCLONE
with good results. It's free for the basic version and very user friendly. You must understand that it will delete any data on the target volume so you may want to backup any important data to some other media. It will give you a bootable clone of the source volume and allow you to boot either volume. There will be no path problem when booting the clone since it will be assigned the C: designation automatically when you boot to it and source drive will then be tagged as the D: drive. With some simple editing of the boot.ini file, you can eliminate the boot choice and boot the bigger drive by default. I think this would be the easiest way to do what your mother wants without opening the box.
If you later want to make it a conventional configuration, it would be fairly simple to open the box and transpose the drive cables. If you never want to do that, that would be fine too. It's quite acceptable to boot the clone and even delete the windows folder of the source drive if you so choose.