The employer may and may not charge you, but employers usually do not tolerate such acts by their employees.
If your family is not trained/well versed in specialized line of the enterprise which they may start banking and depending upon your expertise, they shall need you now and then and you shall not be able to stay away during your employment hours. You may be noticed transacting your private business during your official hours. Any one can whisper to your employer that you/thru your family is starting your enterprise and this shall be more than sufficient to provoke the employer.
A vindictive and zealous employer offended by the employee can go to any extent to chase and hound you to set an example for you and many others. The burden of proving the charge is on employer and burden of proving the innocence is on the employee.
Your family members are free to exercise to enter into any business but you should not be involved directly or indirectly as stake holder or in day to day operations.
You must not poach the clients of your employer and use the official email, company property to transact for the company of your family.
It shall be appropriate to enter leave job first and then enter into business full time to avoid legal complications which your employer can create for you.
