Mom is visiting me in HK from the states and we have booked for Beijing.

My mom is visiting me from the US while i study in HK.

We have booked tickets to Beijing and back to HK for a thee day weekend. Originally I thought we could Use the 72 free period but I did not realize since the literature is rather vague you needed a separate country as your exit from China. Since I am in HK and can apply for an entry permit easily this is no problem. However my mother will need one and she will not be in HK long enough to obtain a visa before we leave for Beijing that I am aware of. How can she apply for a tourist L type from the states when just going to Beijing for 3 days?

I am feeling like going to Beijing was a really bad idea since it is so complicated.
Any advise would be appreciated.
Thank you,
Rose