Am I legally sinful after being acquitted by law of the charge of killing a person whom I had pushed away from myself after he assaulted me, and then it became clear that he died as a result of another assault by his brother?

If the cause of death of the deceased was due to him falling and being pushed by his brother, then the questioner is innocent of murder and nothing is upon him. It is preferable to increase seeking forgiveness (Istighfar), good deeds, and supererogatory acts of worship (Nawafil).