Is there a way to make it that moving the mouse doesn't rotate objects in build or buy mode? I mean you have to use the <> keys to do so. Reason is I have essential tremor (what Katherine Hepburn had later in life.) It always moves wrong for me as my hands shake constantly. Needless to say I can't play FPS or any action type games.

Can you use the enter button to place objects after rotating (I'm not sure)? If so, try letting go of the mouse when hovering over where you want to place the item, rotate with buttons, and click enter. Or let go of the mouse, rotate with buttons, and do a soft click with the mouse if you can (a touch pad button if you are on a laptop works much better because it doesn't move).

I think there exist special computer mice or other options that might be easier to use if you have tremor. Nowadays they make all sorts of gadgets for computers that's supposed to help for or prevent various conditions, so it could be an idea to check around a bit if you're interested.

Nope, enter doesn't place objects.

Are you on a stationary with a regular keyboard, or a laptop with a touchpad (with or without buttons)?

Desktop with regular keyboard.

If you manage to click your left mouse button without it moving anything, you could try the second method - Select the piece of furniture, hover the mouse over where you want to place it, use the > < buttons to rotate, and click to place.

If that doesn't work, then maybe consider getting some sort of trackpad with separate left/right buttons (similar to what you'd find on a laptop). It may give you better control over the mouse placement, since clicking those buttons wouldn't move the arrow around, even if your hands shake. If you use a small mouse, it might also help with a bigger one, since you get more rest for the wrist so precision may be a little easier. This ccould probably also help with other games and computer tasks.

If you're using Windows 10, it's got some settings that might help, for instance voice control, or the possibility of using the numerical keys to move the arrow, and you can make the mouse slower. Not sure if other Windows versions have the same, but it might be worth looking into.

Maybe adjusting the mouse sensitivity might work? Then the game hopefully doesn't register the shaking as you trying to rotate the object.