It can be very difficult to watch a child be aggressive towards, or hurt, another child. We appreciate that you have concerns and applaud you for wanting to find solutions that might help this mother on her AP journey.
API encourages parents to take a holistic approach to determine what might be triggering their child's challenging behavior. There are a variety of issues that might be at work with this little boy. Age and development may make it difficult for the child to express himself in a gentle, clear manner. Perhaps sensory issues or stress in his home life may be the cause. Maybe the child is seeking more one-on-one attention from the mother or the second parent works long hours and is unable to spend as much time with him. Often, the arrival of a new sibling will cause a child to become aggressive. There can be many reasons why a child acts out, and API believes that it's our job as parents to identify the unmet needs of the child and help him express his needs and feelings in more positive ways, rather than punish him for the challenging behavior. Sometimes children seek attention and obtain it through any means possible, including bullying other children. Parents need to watch, listen, and speak to their children to determine what might be the root cause of the challenging behavior.
A great tool for communicating with children and adults is called "nonviolent communication" (NVC). It is a tool developed by psychologist Marshall Rosenberg, and there are several books on the subject, including a few specifically related to parenting. Some great things about it are that it is very simple, easy to learn, and can be used in communicating with people of all ages. Sometimes it is difficult to implement because it is so different from our normal way of communication, but just learning the basics can be very beneficial at changing the way we understand and communicate with others. Raising Children Compassionately is a wonderful booklet that teaches NVC techniques that can be used with children.
I would also recommend reading some articles about living with children on the Natural Child Project Web site to see if anything there might be helpful to either you or the mother.
It sounds like you really want to help this child, but if the parent dismisses the aggressive behavior and doesn't work with you to minimize it, then another solution might be finding an alternate play date location. Another idea is to set up the play date so that children and parents are sharing space and their activities are monitored so that the children's needs can be met and aggressive behavior addressed before it results in tears.