B.G.
Hi C..
The sooner you spend a night away from your daughter, the better for the of you in the long run. My daughter began staying the night at my mom's for one night a month around six months, and now at 18 months, they've got their routine down and she just loves going to visit Grammie.
On the other hand, I nanny for a 20 month old who has never stayed a night away from her mom, until just recently. Honestly, the little girl did great, but I think it was harder on the mom. But at the older age, it would easy for her to play on her emotions not wanting mom to go.
As far as when you leave her, I would kiss her goodbye while she's awake, make sure your mom is aware of her routine... and leave. Let grandma put her down, so she is not anxious waking up and seeing grandma, and wondering where mommy is. You'll miss her like crazy and it will feel very strange going to bed with your daughter not under the same roof, but call a million times if you need to and in the long run you may be able to do it again and enjoy a much needed night to yourself.
Good luck!