You can apply for an open work permit, then can do whatever jobs with the same criteria with locals, except for few jobs like lawmakers.
Your daughter can get her passport, TARF, citizenship in the same way you do, using her grandparents HHR.
Your wife is applied regulations for HKers, and can get a citizenship without renouncing her current nationality.
Instructions for HKers
In Chinese
TARC
https://www.immigration.gov.tw/5385/7244/7250/7296/居留/148063/
HHR
https://www.immigration.gov.tw/5385/7244/7250/7296/定居/41965/