In South African law, both parents have rights and responsibilities towards their children. The law recognizes the importance of maintaining a meaningful relationship between the child and both parents, unless it is contrary to the best interests of the child. Therefore, a mother does not have the unilateral authority to deny a father access to their children without proper legal justification.

If a mother is denying the father access to the children without valid reasons, the father can take legal action to enforce his rights. The first step would typically involve attempting to resolve the matter through mediation or negotiation, with the aim of reaching a parenting plan or agreement that outlines the access and custody arrangements.

If the parents are unable to reach an agreement, the father can approach the family court to seek a court order regarding access to the children. The court will consider the best interests of the child as the guiding principle when making a decision. Factors such as the child's physical and emotional needs, the child's age and maturity, and the ability of each parent to provide a safe and stable environment will be taken into account.

It is important to note that each case is unique, and the court's decision will be based on the specific circumstances presented. Here are some key rights and responsibilities that fathers have in South Africa:

1. Parental rights: Fathers have the right to be involved in making important decisions regarding their children's upbringing, including decisions related to education, healthcare, religion, and general welfare.

2. Custody and guardianship: Fathers have the right to share custody and guardianship of their children, provided it is in the best interests of the child. This means that fathers have the right to have their children live with them and participate in important decisions concerning the child's life.

3. Access and visitation: Fathers have the right to have regular contact and visitation with their children, even if they do not have primary custody. The law recognizes the importance of maintaining a meaningful relationship between the child and both parents, unless it is contrary to the best interests of the child.

4. Financial support: Fathers have the responsibility to provide financial support for their children. This includes contributing to the child's maintenance, such as providing for their day-to-day expenses, education, healthcare, and other necessary costs.

5. Equal treatment: Fathers have the right to be treated equally with mothers in matters related to custody, guardianship, and access. The law does not discriminate based on gender when it comes to parental rights and responsibilities.

It is important to note that the best interests of the child are always the primary consideration in matters concerning fathers' rights. If there is a dispute or disagreement between parents, the court will make decisions based on what is deemed to be in the best interests of the child.

If you are a father and believe your rights are being infringed upon, it is advisable to consult with a family law attorney who can provide personalized advice and assistance based on the specific details of your situation.