Is a person considered sinful for staying away from his family—his mother and two sisters—in another country for work, knowing that his mother encourages him to remain abroad due to the hardship of life, and that his father is deceased and he has no brothers, while his eldest sister is unmarried?

Seeking to earn a livelihood is legislated and required by Islamic law. It is a form of striving in the path of Allah, especially if it is to earn a lawful income and provide for one's family. Indeed, the one who strives for the widowed woman and the needy is like a mujahid (one who strives in the path of Allah). Your travel to toil for your mother and two sisters is a form of jihad and an act of devotion to your mother.