Have you considered getting BT WHoleHome WiFi, rather than going with the Google system? Keep your exisiting router, plug disc 1 of the WholeHome into the router via ethernet cable and then place the other discs around the house in the best locations as directed by the BT Whole App. That should work a charm - I've got Sky Q and everything works just great.
Once I set up the WholeHome system I turned off wifi on the HomeHub, as that seems to be the recommended approach. Obviusly, all your devices then need to be connected to the new network.
Edit: I've just seen Keith_Beddoe's post... I'm not sure if the same applies to the BT WholeHome System (I don't have BT Sport, but I do subscribe to the complete Sky Q package and, as I say, it works perfectly.
The BT YouView box would have to be connected directly to the home hub, or via a couple of BT Mini Connectors. Apart from that, the BT Whole Home system should be fine.
I have a the BT whole home WiFi system and works great and to clarify the BT YouView box we use is plugged directly by ethernet cable into back of one of the discs in a bedroom. So we havent used a LAN Plug or direct ethernet from router to the YouView box.
Our set up is :-
Draytek Vigor 130 - Modem
TP-Link TL-R600VPN - Router
BT Whole Home Wifi plugged into the Router
This has been far more stable than the BT Hub 6 and better WiFi overall