Well, FWIW both of our sitters have driven my kids in their car - mostly for drop-off/pick up of their own kids. I never got a driving record - but I trust our sitters. Maybe I shouldn't, but I also see how they drive with their own kids. Since my first sitter did a lot of driving - we just have seats for the sitter's car. I install in their car and periodically check them for tightness etc. Both of these women are driving with their own children at the same time...so I know they are being safe. That said, our first sitter was in a fender bender when another car slide on a snowy road and hit her while my kids were in the car. She called me immediately and everything was fine.
Maybe I'm a little too lax, but I feel that these women are as responsible (maybe more some in some measures) as I am....so I'm not terribly concerned. I do insist on providing the carseat and installing it. I've run over how to use it properly, but again, these are women with kids of their own and understand the importance.
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DS - Adopted by loving parents 1995
DS1 7/2009 ('Stachio)
DS2 9/2011 (Peanut)