My sons both went through phases where they were really unhappy when the woke up from naps. (They also went through that awful phase where they no longer napped but were really cranky when I was trying to make dinner!)
You didn't say if your babysitters watch other kids, but in a day care environment, your daughter probably just has to go along with the group. She wouldn't get as much specialized attention from her babysitter because there are other kids around and the sitter can't drop everything and hold her. Chances are that there is some sort of activity to become involved with.
So it almost sounds like you are trying to be too hand-on with her when she wakes up. Things I would suggest trying:
1. Try to figure out why she doesn't nap as well at home. It sounds like she is still tired when she wakes up.
2. Having a favorite activity at the table that she can do on her own.
3. Watching her favorite show on TV while she cuddles with a favorite blanket or stuffed animal so she can wake up more slowly.
4. Routine, routine, routine...make sure you're doing the same thing each day when she wakes up. Chances are the sitter has a routine so your daughter knows exactly what to expect when she wakes up.
5. Let your daughter know what she should expect to do when she wakes up. She should know what comes next and what your expectations are. She might not understand all of it, but telling her that she shouldn't cry when she is crying is not as effective as doing it before she gets upset.
6. Feel free to recite my mantra of motherhood: "And this too shall pass, and this too shall pass..." Deep breathing and happy beach scenes in my head always brought a feeling of calmness. ;) Good luck!
M.