Hi dschaareman,
Welcome to post in Microsoft Community. I'm Mosken, let me help you figure it out.
According to your description, I knew that you find out that screen time in your child's computer doesn't work, so you have to set screen time every time the computer starts, and you don't receive a weekly activity report. Is that right?
It is recommended that you first check your computer and your child's computer for system updates. On the desktop click "Start" > "Settings" > "Update & Security" > "Windows Update" >"Check for updates".
Then it is recommended that you try to remove your child's account/device from the Family group first, and then try to re-add the account/device.
Then about the weekly activity report, please make sure the feature is turned on and "Email weekly reports to me" is checked.
The following link is about Screen time and activity reporting, you can try the solutions, I hope it will help you.
Fix screen time limits not working(microsoft.com)
Fix family activity reporting for Windows 10(microsoft.com)
The above steps are provided based on the information I have learned so far, I wish that will be helpful to you. If your problem still cannot be solved by these steps, you could tell me the specific situation in the next reply. I will continue to assist you in solving the problem.
Best Regards,
Mosken- MSFT | Microsoft Community Support Specialist