RE: "No! I want Mommy/Daddy to do it!"
VERY familiar except in our household, it's almost always "I want mommy." This is mostly about dissing Daddy when he spends too much time away from home, which happens way too much.
I and friends have also encountered a lot of this when the mom is pregnant and the child is trying to cling to a familiar role. Sometimes daddy becomes the desired one beacuse he's not tired all the time; sometimes mommy becomes the desired one because she seems to be less available to the child.
We accomodate our daughter if it is easy for us and we are feeling tolerant. If my husband was feeling too dissed or I was too unwilling to do whatever she was asking, we'd say Daddy was going to do it or it wasn't going to get down. Sometimes we'd tell her to change the way she was talkng to not be so rude. She's usually cry and walk in unhappy circles for a few minutes before deciding that daddy doing it was OK.
It still happens, but a week or two of reacting as I described usually improves it.
Advice and commentary on living overseas
DD1 15, DD2 12, and DS 9