"If the Opposition won the majority in the Senate, would they sit on the right of the President?"

Thanks for your question.

As you know, at an election the party (or coalition of parties) with the support of the majority of members elected to the House of Representatives becomes the government. That team will sit to the right of the Speaker in the House of Representatives, and to the right of the President in the Senate. So even if the opposition had a majority in the Senate they would still sit to the left of the President.

diagram to help explain If the Opposition won the majority in the Senate, would they sit on the right of the President?