We went/are going through this at bedtime, but I can tell you what helps/is successful for us and I hope it helps you, too.
My almost 2.5 y/o goes to bed with his papa. He's been doing this for about 6 months. We started this because 1) I'm more likely to clean up the house while they're doing it, 2) we're expecting our second and I expect to have to do most of that bedtime routine.
Anyhow, so this (the needy lil'n) happens 1) when DS is tired, 2) has had the opportunity to spend lots of time playing and having fun with me and DH has been busier than normal. It's pretty much what you describe. DS cries and asks for me, DH tries to do the things for him anyway.
We discovered by accident one night when I had an evening meeting that when I am absolutely not there, things run incredibly smoothly for the two. On the subsequent night that we discovered this, I went out again to the movie store (I had no desire to rent a movie and ended up reading half a book heehee). After that, as long as I'm quiet and don't exaggerate my presence in the house, they work out bedtime quite well without me.
I don't know if any part of this scenario is applicable, but it seems similar to our issue.