Re: Parental control does not send request via messages: What should I do to get those requests via messages?
Apple Support's online article: Set up Ask to Buy - Apple Support
says: "Where to find your Ask to Buy requests
If you miss an Ask to Buy notification, you can find the request in Messages on your iPhone, iPad, Apple Watch, or Mac. If you don't see the request in Messages, you can find your Ask to Buy request in Notification Center. Learn how to open Notification Center on your iPhone, iPad, or Mac "
You may want to check the settings you have chosen in notification centre.
See if you have turned off message notifications / You can assign a special sound for certain contacts so you know when you get a message from them. Change message notifications on iPhone - Apple Support may help.
To check the devices of the children whose messages don't appear in your Messages app:
Change notification settings on iPad - Apple Support
or
What to do: If you can't send or receive messages on your iPhone or iPad - Apple Support
Hope something here is helpful :-)