We both had items we couldn't compromise on, but I was willing to meet one of their demands and in return they did the same for me.
この場合、次のような言い方ができますよ。
ーWe both had items we couldn't compromise on, but I was willing to meet one of their demands and in return they did the same for me.
「お互い譲れないポイントがあったが、相手の要求を1つ呑む代わりに、相手も私の要求を1つ呑んだ」
items we couldn't compromise on「お互い譲れないポイント」
to meet one of their demands「彼らの要求を1つ呑む」
ご参考まで!