My father passed away in his own home where he lived alone while a caregiver watched over him.
While his carer watched over him, my father passed away in his own house where he lived by himself.
お悔やみ申し上げます。
日本語で「誰々が死にました。」と言うより「誰々が亡くなりました。」と言った方が丁寧みたいに、英語でも “Mr. So-and-so died.” と言うより “Mr. So-and-so passed away.” と言った方が丁寧です。「一人暮らし」は “live alone” とか “live by oneself” と言います。お父さんの希望を英語で説明したい場合は “It was my father’s wish that he would pass in his own home and not at the hospital, so he hired a caregiver with his nursing insurance to come to his house regularly.” （父は病院ではなく自宅で死ぬ事を希望し、介護保険を使って、ホームヘルパーに定期的に来てもらいました。）と言います。
アメリカ合衆国 
