Why does my baby cry with the babysitter?

Many reasons. Hunger, pain or missing her mother.
Separation anxiety. It is very common for babies to cry when they are with a person who is a stranger, or when they are separated from their parents. In this case, both things are happening at the same time: you are separating from your baby and putting her in the arms of someone she doesn't know as well. Over time, most babies will out grow this and will be more comfortable around people less familiar to them.