Separated is for people who no longer have lives in common. Lots of families have parents in two different cities/states/countries because of work or personal reasons.
Admissions and financial aid offices are familiar with this kind of situation. For now, use the address where you and your mom live. Then let each of the places on your list know that your parents reside in two different countries, and ask the admissions and financial aid offices if you need to send additional information. Don’t be surprised if each place asks for something different.