Depends on how big your D Drive is.
There's not much difference playing TS4 and TS2 on SSD or HDD. Possibly only the booting time for the games will be a tad bit slower on HDD.
If you are going to move your files, I suggest just copying your The Sims 4 folder (the one with the saves and mods and tray) and move it to the desktop.
Then uninstall it and make sure you change the path in your Origin to re-install the new file in the new drive.
I believe there's a faster way of doing it without having to uninstall the game, but I would suggest you do anyways if you have time and wifi. Maybe @rosemow knows the shortcut.