You don’t need to wait for your parents’ permission to go out for work or important matters such as meeting someone in a clean environment or shopping or banking or other important personal issues.

Parents have no right to restrict your movements; their right over you is limited to help protect your honor and dignity. As long your travel is not involving long distances where there are valid reasons for your safety and security they have no right to object to your free movement.

I think the challenges you are facing from your parents are more to do with cultural issues rather than due to sound religious teachings.

Many people today confuse culture with religion. Religion is a set of spiritual and ethical norms meant for all times and cultures; whereas culture and customs are time bound and hence alterable.

Allah Almighty knows best.