Daughter having my old handset

The best course of action is:

1. Make sure that you no longer need any data on the iPhone 5S. They will be deleted in the next steps. This won't be an issue if you synch your iPhone through iCloud.
2. Follow Chattanoogan's recommendation above to reset your iPhone 5S to factory settings (section "If you still have your iPhone, iPad, or iPod touch" in What to do before you sell, give away, or trade in your iPhone, iPad, or iPod touch - Apple Support)
3. Set up the 5S as a new phone (Set up your iPhone, iPad, or iPod touch - Apple Support) and make sure to enter your child's Apple ID when prompted.
4. Review the Family Sharing settings for your child on your own iPhone to make sure that they are correct. In particular, make sure that her Apple ID is correct. If not, remove the wrong Apple ID (Leave Family Sharing - Apple Support) and add the correct Apple ID (Set up Family Sharing - Apple Support). You may also want to review some of the parental controls.

Then you should be able to locate your child's iPhone 5S: Locate Family members’ devices using the Find My app - Apple Support

There is a better solution: Family Sharing. Please see the following article on how to set it up: Set up Family Sharing - Apple Support

Then you should be able to achieve what you are seeking: Locate Family members’ devices using the Find My app - Apple Support

You need to “scrub yourself out of the phone” and then set it up “new” as her’s w/ her own unique AppleID.

Follow the steps listed in this article for the “scrub”

https://support.apple.com/en-us/HT201351

From what you've told us, your child was not part of Family Sharing.

If they are: Leave Family Sharing - Apple Support. Then set up up their iPhone as described in the links above

If they were not, turn off Apple ID on their phone ( Settings > your name > Sign out). Then proceed with the steps in the links above.

Sorry, I must have missed sending you this article: Create an Apple ID for your child - Apple Support. It will tell you how to separate (and control) what your child has access to.