You are sharing an Apple ID with your daughter would be my guess. You need to assign an email address on your daughter's iPad that she can use as her contact at email address for the Messages App.
Watch this video for help on this.
Using FaceTime http://support.apple.com/kb/ht4319
Troubleshooting FaceTime http://support.apple.com/kb/TS3367
The Complete Guide to FaceTime + iMessage: Setup, Use, and Troubleshooting
Troubleshooting FaceTime and iMessage activation
Using FaceTime and iMessage behind a firewall
iOS: About Messages
Set up iMessage
Setting Up Multiple iOS Devices for iMessage and Facetime
FaceTime and iMessage not accepting Apple ID password
Unable to use FaceTime and iMessage with my apple ID
For non-Apple devices, check out the TextFree app https://itunes.apple.com/us/app/text-free-textfree-sms-real/id399355755?mt=8
I use the same Apple ID on 3 devices of my own and 2 belonging to my wife and daughter. I set up additional email addresses for all of us to use on all of the devices.
My wife and daughter have their own email addresses anyway - as does almost everybody these days - so it wasn't like I had to create new email addresses for them to use. I have 5 email addresses so, I had plenty to go around for my 3 devices.
It is really pretty easy. You will figure it out. Good luck!