What are the legitimate legal rights of the second wife in this situation, and how can she deal with her husband's family and manage her affairs, and what is the ruling on her working without her husband's consent under the mentioned circumstances?

The second wife, even if she does not have children, has the same rights as the other wives. Rights do not differ based on children or seniority. If a husband dies and leaves two wives, each of them receives half of one-eighth of the inheritance. What the husband gifted to his wife while he was in good health and she took possession of it is her right, and no one may demand it from her. She may relinquish it if she sees a benefit in doing so. The sister should treat her husband's relatives well and respond to their ill-treatment with kindness.