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I presume that by "HK passport issued in China", you are referring to the Exit-Entry Permit (往来港澳通行证). If so, standard procedure would be that you exit China using the EEP, enter Hong Kong using your second passport, and then you can exit and re-enter Hong Kong freely (assuming your second passport has visa-free rights to HK).
The problem you will have is that the EEP limits visits to Hong Kong to 7 days. So the above works for trips <7 days in total, but if you are away for three weeks and then cross the border back from Hong Kong to China, China is highly likely to notice that you have overstayed and then you will have a hard time explaining why and how.
I would advise getting a full Chinese passport and using this to travel via a country that does not require advance visas, such as Thailand or Indonesia.