Is the questioner accountable for the sin of the death of her mother's husband and her uncle, who passed away ten days after she hit his swollen arm with a chair, knowing that he had been abusive towards them in the past?

If your hitting your uncle was in self-defense or in defense of your sister, and he was the aggressor, then there is no sin upon you and no liability; because it falls under the category of repelling an aggressor. However, if the hitting was for revenge for a previous offense and not a current defense, and your hitting caused his death, then this would be considered akin to involuntary manslaughter ( قتل شبه العمد ) if it is proven that death was caused by the hitting through the spread of the injury, and specialists such as forensic doctors would rule on this.