I would suggest that you stop rebooting your Homehub. This will cause you more problems as DLM (Dynamic Line Manement) will see it as an unstable line and lower your speeds.
If you have a look through the forum you will see that there was a problem with the HH5 latest firmware update. If you leave your HH5 connected 24/7 it will upload a fix for that.
See this link regarding problems with Samsung TVs.
Parental controls work at a network level so they will block all devices that use your Homehub. Have a read through the help pages.
I assumed you were meaning the parental controls because you mentioned "parental" in your question.
I have never used access controls so I may be wrong but I believe that the access control does not switch a device off the Homehub if it is already connected when the "switch off time" comes around. If the device is already connected it stays connected.
If the device is not already connected when the "switch off time" comes around it is unable to connect.
Not an ideal situation as it would appear that you will have to ensure that your child's device is disconnected from the Homehub first in order to prevent it from reconnecting.
I have just re-read this thread again and it would appear that my eyes are painted on as I have totally misread it.
While I believe access controls acts as I have outlined above it should only block individual devices and not every device.
I would try a factory reset of the homehub by pressing a pin into the recess button on the rear for about 20 seconds. This should clear any configuration settings that may have been corrupted during the update on 15th Jan and also any that may have occurred in any subsequent update fix. . Once this has been done set up the access controls again.
The moderators of the forum have been informed of your problem. Once they have read this they may be able to help. They are a BT UK based team and if they can help they will reply via this thread asking you to contact them via a link. Once you have replied to them by the link, it can at present take up to five working days for them to re-contact you.
I am sorry to hear about your problems with the hub. I can take a look into this for you.
Please send me in your details using the "Contact The Mods" link found in my profile and I will be in touch.