V.W.
I didn't experience this myself... except once. My little one cried when we left "Nana's" once. We had been visiting and she wanted to STAY AT MY MOTHER's when the rest of the family was leaving to go home... we live 6 hours away... I was a tiny bit hurt that she wanted to stay with my mom than go home with us... but it only happened that once. She had been having a great time with my mom though, and Nanas know how to spoil and give that one-on-one attention that they crave at this age.
So, I would just say: 1) it's a phase she will outgrow; and 2) try to make it more fun for her. What I mean by that is, she is playing and doing fun stuff with lots of attention when she is with her sitter, right? When you come to pick her up, she has to stop whatever it was she was doing. They especially need help transitioning from one activity to another at this age, too. So, maybe address that with the sitter, and try to build a few extra minutes into your "pick-up-time" routine, so she can complete something she is doing or know that "in 5 minutes we will be getting in the car"... Then, when you get home, try NOT to get straight down to work (dinner, chores, etc). Make time (even 15 minutes will help) to play with your daughter. And tell her as you're packing into the car what you have planned for when you get home... "Guess what we get to do when we get home today?!.... We have some brand new purple play-doh!! And I want you to help me make animals with it.... Does that sound fun??" Try to get her to anticipate something fun when you get home.
Learning to transition is a big part of growing up. Start now in small steps. As she gets older, you can be more grown up about it too... " Two more minutes on the swing, then we have to get in the car and go ___"... And when they are old enough for computer time it will be the same thing.. "5 more minutes, then you have to get up."
Just try not to take it too personally right now. She spends a lot of time with her sitter and probably has a firm bond with her. That is a GOOD thing. The separation anxiety is a normal thing.
Best wishes...