Russian Instrumental Case
Russian verbs, adjectives, participles and nouns can be used with different cases. The short participle озабочен (озабочена, озабочены) are always used with nouns and adjectives Instrumental case.
Отец был озабочен результатами экзаменов. Father was worried about the results of the exam.
Матери is the Genitive case because your phrase can be translated (literally) as "She was worried about leaving of her mother". All the expressions used with the preposition "of" in the English language in the sense of possession are used with the Genitive case in Russian.
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