Perhaps you could consider choosing your babysitter now and having her come over a couple of times a week to get to know your child. (Gives you some free minutes to use up too!) Then after a few visits between the sitter and your child, make the visit time coincide with nap time and have the sitter put her to bed for the nap. Do this a few times and see how it goes. Then do a few nighttime sessions when you are at home (pay the sitter , but be there). Then a do a couple where you leave the house and the babysitter and your daughter are on their own, but you're available if needed.
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My situation is not exactly like yours, but there are similarities. My husband and I have parented my 2 year old in a very attached, connected way. She has slept in our bed from birth (when she was born I held her for a month straight night and day). She is VERY well adjusted, calm, and adventurous. She is not spoiled, whiny, fearful or needy. I attribute much of her character to the connection she has in our family. Anyway, tonight is her second night of not sleeping in our bed. We are lucky to have teenagers and have decided to transition her out of our bed into a bed of her own via her sisters bed. :-) The first night that she realized she was going to be sleeping in sissy's room she put up a big fuss. (big for her - about 10 minutes) But sissy told her to go pick out a book, give everyone a kiss night-night (our long standing routine) and off to bed. She did sleep there all night and big sissy was a trooper about it! Tonight when it was bedtime, sissy said, "Get a book and kiss everybody". My toddler said "No" and slumped to the floor. Sissy encouraged her again and she started to fuss, but got the book and off they went. When my toddler realized she was staying the night in sissy's room again she cried for Mama and Papa for a couple minutes. Then everything was quiet. And right now it is still quiet, so I am assuming everything's good. :-)
I know its not the same situation as yours, and my daughter is older and more verbal, but I guess the idea I'm trying to get across is that gradual, positive experiences and not waffling about it will probably produce good results for your well-nurtured child.