Here are some ideas: temporarily put your son to bed in his portacrib somewhere else in the house and let her yell it out. Tell yourself, "I am the adult here, so I am able to control my anger." Look at the big picture, soon this will pass and it will work out if you regain the upper hand. Talk to her as if she understands you in a calm voice, "We will only pick up your teddy one time, if you throw him out again we will not come in and give it back to you" Then, follow through, when/if she throws it out, go in and say, "If you throw it out again, I will not get it for you'. Crying it out is easier if you pop your head in after 5min, without saying anything, just to let her know you're still there. If she continues to cry,pop in again after 10 min, and then again after 15 min. So that is approximately 1/2 hour of crying time and most kids quit before that. Also, during the rest of the day, speak to her desire to be with you, "You miss being with just Mommy, don't you. I miss being with just you." The other moms will have some ideas for how to spend more one on one with her.
As far as her taking up so much of your time during the day, and I think that is your real frustration, try not to react to her shenaningans with anger or false interest, be matter of fact and either ignore them or take care of them while speaking in a normal tone of voice. You know she understands a lot of what you say so over and over say things like, "I want to spend time with you in fun ways, not with this silliness" "It doesn't really matter if you get..." "I have to feed the baby now, and I know you understand that" Let her be your little helper with the baby. "If you keep whining at me it makes me feel tired, please stop" then add a dramatic demonstation of your tiredness, like hanging your head down, or putting it on the table. "I need to have some quiet time, you sit here and look at a book." She will respond to the genuineness of your words and tone. Some times adding some dramatics that kids understand helps her understand your meaning. This is about communication, and with a child whose language abillity is still minimal. Throw your arms in the air and look amazed and say, "Again, you want me to do ... for you again!' Have your husband read these responses.