transit visa 144 hours

Hi
I am Polish citizen can I fly without entry permit with my family 2 adults 2 kids plus infant from UK - Beijing (5days)-HK then stay 5 days in hong kong and Makau take a train to Shanghai (3 days) and fly back to UK?

So I will have flights
UK-Beijing
Beijing to HK
Shanghai to UK

I reasume I will qualify for 144 hour transit as I will enter beijing from UK and fly to HK and then from HK train to Shankghai and fly to UK

What do you think?
I can not risk with kids and entry permit from london for 5 people will be expensive ;(

Please help
Karolina