Try making it a game, when you ask to pick up her room, make it a game and reward her, stickers worked with my three year old son. For potty training I gave my son his very favorite candy everytime he went to the bathroom and then I followed by saying what a big boy he was and gave him positive reimforcement. I do not think yelling or spanking her hand helps. Time outs work as long as your consistent.
I agree be consistent and ignore tantrums if they are not harming themselves or others.
Time-out does not work b/c it accomplishes the very thing she is trying - to get out of whatever you ask her to do.
For such a small child, wait 10 seconds, repeat your request, wait again, if not done, take her hand and lead her to the place you want her to be and prompt to complete the task. Be very consistent. Ignore tantrums
Good luck