Is it permissible for a woman to travel with her mother and her brother, who will return to his country in a few days, while her mother's paternal uncle is in the country she is traveling to, and her maternal uncle will arrive after two weeks?

What is prohibited is a woman's travel without a mahram, not her residence without one, if she is safe from temptation. So, if your brother will travel with you, and your mother will stay with you during the course, there is no harm in your participation, as long as it does not involve anything forbidden, especially with your maternal uncle and your mother's paternal uncle being in that country.