Dreams involving family dynamics, especially after significant life events like the passing of a parent, can be deeply emotional and revealing. Your dream may reflect feelings of loss, insecurity, or fear of being replaced or overlooked, particularly in light of your father's death.

The new child in your dream could symbolize feelings of inadequacy or a fear that your parents' love and attention may have shifted, especially after the loss of your father. The imagery of running away from your mother while she tries to catch up may suggest a desire to distance yourself from these feelings of competition or inadequacy.

The rainy puddles can represent sadness or emotional turmoil. Walking home alone might indicate a sense of isolation or the struggle to find your own path after a significant change in your family structure.

Overall, this dream could be urging you to explore your feelings about your family's dynamics, your role within it, and how you are coping with your father's passing. It may be helpful to communicate openly with your family about your feelings, as this can lead to understanding and support during this difficult time.