Hello,
Here is my concern. My wife and I have a work permit. We do have a SIN both of us. Now our daughter found a part time job but she does not have a SIN yet. Do you think she could apply for a SIN. She is 16
Thx
Simple answer is: does she has a work permit? - No. So she cannot work and won't get a SIN.
You and your wife have work permits, so you both can work legally.
Your daughter is an individual, so unless she has her own work permit, she cannot work.
If she apply for post secondary study permit (and show to be able to afford international student fees and living), then her study permit will allow her to do part time work. (some study permit doesn't, you need to double check)