In that case, find someone LD may go to preschool with (keep fingers and toes crossed that they get along) and go to daycare together. By the time of preschool, they have been pals for a long time. At least they will have someone they know in a new place.
Some preschools have smaller kids class. Staying in the same building will be a lot easier for LD when preschool comes.
However, if LD is sick, daycare will send him back home to you. A sitter does not have this problem. Not everyone can affort that kind of emergency. That is one of the major reasons people opt sitter.
Another word, if he does not like the sitter, something might be wrong. If she loves him enough, he should not behave like that. It is hard on him not able to tell you what is going on. Trust your gut feelings and trust LD.