Can I apply for a work visa or a student visa if I am on a B1B2 visa with my family?

If you are in the U.S. and in-status (B-1/B-2) you can certainly file to extend or change your non immigrant visa status. However, the query is what to change it to. If you are changing to a work visa that would be hard since there are few classifications that would be available. If it is a student visa you are seeking, then you can try to change in the U.S. or take the I-20 to the Consulate abroad for a stamping. There are many nuances to the information you seek and it is a good idea for you to consider enlisting the services of a qualified immigration lawyer or legal counselor.