Data being sent to old and new iphone
On your old phone, go to Settings > Messages and disable iMessage.

On your new phone, go to Settings > Messages and check if text message forwarding is enabled; check what devices are selected as recipients and remove the old phone if it is there.

Better yet, reset the old iPhone:


Go to Settings > General > Reset > Erase All Content and Settings
Set up your iPhone as new.
Create a new Apple ID to your grand child.


She will have her own Apple ID to set up iCloud and other services independently (for instance, saving and migrating game progress with her account).
You will have separate iCloud accounts and passwords; photos and other personal information that may end up mixed is now on different accounts.

The only disadvantage is that she will have to download the games again and start from scratch.

Optional: Set up Family Sharing.


Go to Settings > iCloud.
Tap Set Up Family Sharing, then tap Get Started.
Confirm that you want to be the family organizer and that you're signed in with your personal Apple ID.
Follow the onscreen instructions.


You can then invite her to your Family:


Go to Settings > iCloud > Family > Add Family Member.
Enter your family member's name or email address.
Follow the onscreen instructions. 


If she is younger than 13, follow the instructions described here: Family Sharing and Apple ID for your child

Setting up Family Sharing will allow you to share games and other apps with her (you don't have to buy them again).
You can also set up restrictions if you need to.