Confused what visa i need or can apply for!

Hi there, my partner and I have booked a holiday to China and Hong Kong from Australia and have now been told we won't be granted visa's. Our itinerary says we fly into Hong Kong, then onto Shanghai before heading back into Hong Kong for New Years Eve and then continuing our private travels .. I am aware that I can apply for dual entry ones but am concerned we wont be granted any one as we are going back and forth. Also, we are not travelling as a part of a tour group, so are unsure how we would get invited? We have booked through a travel agent in Melbourne, Australia if that helps and have no criminal record or anything like that... Hopefully you can help!