Just a note about texting...I have Sprint and when I was on the Fascination in November, it was $0.50 to send a text and $0.05 to receive a text. Then, on the Elation last week it was now $0.15 to send a text, so the rate changed.
Either way, the cost of sending a few text messages every day are negligible compared to the cost of your cruise and the piece of mind you will get is priceless.
My wife and I have cruised many times while Grandma watched the children for us and we never had a problem, although, four years ago, when we got to St. Thomas on the seventh day and had cell service, we found out that everyone had had a stomach virus and had spent multiple days throwing up. We felt bad, but everyone was OK. Just remember to sign a letter before you leave, giving the caretaker permission to seek medical care on your daughter's behalf. That is very important.
The bottom line is that you really shouldn't have to worry, if you really trust the person you are leaving your child with. If you don't trust them, why would you leave your child with them? Grandma will do just fine!
I hope you have a great cruise!