L.L.
You just have to stick with it. We have a new 12 month old coming into our nursery at church. The first two times she was in, she was just like your daughter...got herself SO worked up she made herself sick, and that's with workers who LOVE children and are very experienced. By the third time, she cried full force for five minutes, whimpered for another five, and then started playing. Fourth time...little whimper, then play. I imagine tomorrow she'll just play. :)
My own daughter was a terrible screamer when I'd leave her in the nursery (she's 17 months old and has not had ANY babysitter yet) but now she's just gotten used to it and screams for about five seconds after I walk out, and that's it!
I'd be more concerned with leaving your children with your mom if you feel she's so terrible...and wouldn't you have known that, seeing as she's your own mother? Just curious.
Hope you find a good sitter. :)