I think this is a difficult situation for many of us. We know how we want our children to be raised, what routines we like to follow, etc. But I think it is important for our sanity and for our children's development to let go a little. We need a break now and then, and our children need to learn to interact with others and develop trust in others. If it is something you struggle with, do it in baby steps.
A few things that may help:
Write down a list of things that are important to you in caring for your child (bedtime rituals, when to change diaper, how long to nap, no peanuts, etc). Then decide which of those you can be flexible on to allow the babysitter a little wiggle room. Decide also which ones must be adhered to. Discuss emergency situations with them.
Invite potential babysitters (whether they be family or not) to the house to watch your child while you do something in another part of the house. Make yourself stay away from them for 5 minutes, then 10 minutes, etc.
Recognize the positive effects the babysitters have on your child's life. My in-laws stayed with my son (then 14 mo) while I was in the hospital for the birth of my daughter. When I came home he was drinking from a sippy cup and had bonded with them (we lived 5 hours away so he had never spent much time with them). My parents took care of my daughter (then 14 mo) while my son was sick in the hospital. She now insists on and enjoys a morning snuggle with one of them while watching a video when she stays at their house - a routine that happens only at their house.
Of course listen to your instincts if you feel someone isn't a good candidate to babysit because they are negligent, absent minded, feeble or they don't take your concerns/requests seriously.
