Was in the same situation before (destination PVG), my case is even more complicated (got married and changed my surname and but didn't update the HKID/SAR passport):
You need to show your UK passport + return permit. Your wife can get on board, then when she goes through immigration, she only needs her return permit. They will ask which flight she is coming from, just tell her the airline.
When she leaves, she will be asked to show another ID rather than the home return permit, I showed the officer my HKSAR passport (the best document since it's doesn't require a visa to travel to the UK) together with my BP.
Your wife will be through before you - so make sure you agree on a spot for her to wait for you, or she can meet you at the luggage belt.