I haven’t read that you’ve done this but forgive me if you have: Have you tried to see if there’s already a load in the wash or dryer that’s finished? I had something similar happen to me before - sim would stand and wave, walking around aimlessly or dropping random piles of clothes usually in front of the wash or dryer. I found the reason being was that the machines already had a load in there and you had to transfer it to the other machine or take it out of the dryer.
Idk if this will work because Sims 3 can be glitchy to kingdom come so in all likelihood I am wrong :D