If everything else works, the problem appears to be with the Mac, not the hub. Try turning off 5G wireless on the Mac.
If you increase the HH5 DHCP lease time, you may solve the problem. It sounds like every time the lease expires, the Macbook loses connection, and connects to BT Wifi.
You also should be a way of removing the BT Wifi connection from the list of stored connections.
As far as I know you can't turn 5Ghz off on the Mac. It's turned off in the HHub and 'I think' that would have to be a HH5.
The Homehub 3 does not transmit the 5Ghz frequency so it is unlikely to be your problem.
Which is why I suggested trying turning it off on the Mac in case it was somehow trying to connect with a 5G signal which doesn't exist on the HH3 and getting confused. As Apple devices seem to be easily confused.