Tricky. I would say pick your battles. They are very much still in their own worlds at 3, ie don't really take others feelings into account, it's all about them and what they want.
I often give conditions- eg "you stay downstairs, I need to go and settle the baby (well baby's name here), DD "no, I want to come upstairs". Me: " Ok, but if you come upstairs you have to be quiet and not talk to the baby as she is asleep, do you understand" DD "ok", Me "so, no talking to baby?" DD "yes, no talking to baby". Bargain made and hopefully carried out!
Or....... I offer something more attractive if really don't want her with me, you can "x,y or z" whilst I do this...... or "No, you stay downstairs, if you stay downstairs and are good then you can do x, y or z when I come down again" (bribery I guess!).
There are some times when it's "Do what Mummy says" however, and the punishment ultimately for not doing it (after warning and 3,2,1) is "go to your room" (this is the worst punishment in our house, and comes from having older DS 5 as well, who age 3/4 had to go to his room a fair bit, but somehow touch wood doesn't seem to have to (age 5) anymore, touch wood, touch wood!)