Please be sure not to tell our rival company that we are doing business.
We don't want XX company to know about our business dealings with you.
この場合、次のような言い方ができますよ。
ーPlease be sure not to tell our rival company that we are doing business.
「ライバル社に我々が取引をしていることを絶対に言わないでください」
ーWe don't want XX company to know about our business dealings with you.
「XX会社に御社との取引を知られたくありません」
ご参考まで！
カナダ 
