Not only my parents but also my older sister is opposed to my opinion.
Literal
Parents [just-だけ] [not-でなく] older-sister [also-も] my opinion [to-に] opposition is.
~だけでなく~も means 'not only X but also Y' — a useful pattern for expanding the scope of a statement. 反対である uses the formal copula. The sentence escalates the opposition from parents to include the sister.