Is it Islamically allowed for me and my younger sister, who are not joining our parents and siblings on an Umrah trip, to be left alone at home for around 10-15 days?
Your parents are responsible to look after you and your younger sister and be sure that you are safe. If their leaving you alone can cause insecurity or danger in you, your parents should make full arrangements to protect you and ensure you full safety. You should your parents to consider your safety before they travel and leave you alone.
'Wassalam,