Hanoi-Beijing-Hong Kong

Hi
I will hopefully be visiting Beijing for 2 days next month. I will fly Hanoi (Vietnam)- Beijing and then Beijing-Hong Kong 2 days later. The tickets will be booked separately. Will I be accepted for the 72 hour transit visa? I will deliberately make a 2 days stop in Beijing before coming down to Hong Kong. I'm not sure if this is allowed (i.e I am not just transiting by chance) and would rather know in advance. Also, is it difficult to sort the transit visa at immigration in Beijing Airport with the staff speaking limited English?

Thank you so much