Hello Ninjadiver07,
Thank you for using Apple Support Communities. Sounds like you're not getting prompted to approve purchases when your child tries to make a purchase. If so, we'd like to help out. We'd like to check and confirm your settings are correct. On your new iPhone, navigate to Settings > Family. In this section, do you see your name still listed as the Organizer? If so, please make sure that Purchase Sharing is turned on. This will allow you to tap on the family member's name to see if Ask to buy is enabled for their account.
Another possible step you might want to try is to confirm your new iPhone matches the name of your old device. Go to Settings > General > About > Name. If needed you can try to update the name as well: Change the name of your iPhone - Apple Support
Just in case, here are a few more steps you can try:
1.) Restart all affected devices. This can help refresh things.
2.) Update affected devices. Keeping devices fully updated can help resolve various issues.
We hope these steps are helpful. Thank you for using Apple Support Communities. Cheers.