This is because you use 1 Apple ID for several different people.
That's why it doesn't work. The reason it goes wrong is because your Apple ID thinks it's your own iPhone that you're trying to share your location from - therefore it only shows the one you've chosen. In general, it is not optimal, or in any way intended for several people to use the same Apple ID. You will only experience problems with that solution, and you have already encountered the first one.
If you want to solve your problem, you must create 1 Apple ID for each person. You can of course keep your current self, but create a new one for your children. Once you have created an Apple ID for them and signed in on their iPhone, you can use Family Sharing to keep track of which apps they can download, just as they can use the ones you have already purchased on your current Apple ID. You can also follow your children in People in the Find app, set screen time restrictions, etc.
First, create an Apple ID for each of your children (Under 13 years):
Create an Apple ID for your child - Apple Support
Create an Apple ID for each of your children (Over 13 years):
How to create a new Apple ID - Apple Support
Read more about Family Sharing here:
What is Family Sharing? - Apple Support
Read how to share location with your family here:
Share your location with your family - Apple Support