My mother in law is elderly and recovering from a stroke four years ago and then pneumonia more recently. She is still weak and needs assistance. My father in law has just returned to working as a letter carrier for the US Postal Service after having taken a month off to provide the assistance his wife needs. Recently, their nephew arrived from the Philippines (legally, as he has a tourist visa) to continue providing care. The nephew recently graduated from nursing school in the Philippines and also passed the nursing board exam there. While a convenient coincidence, he has shown that he is up to the task.

Is there a way to petition him to be the caregiver for my mother in law?

Caregiver is not considered "specialist/expert", not qualified for employment visa.