“we are saved by grace alone, but the good works we do are the result of our faith in Christ and our relationship to Him”
Friend, that’s precisely what I believe. That’s protestant doctrine. That’s what your church wanted to kill Martin Luther for teaching.
Yes, we are indeed friends - siblings in fact - in Christ. I think we often focus more on what separates us than what joins us. Judgements were harsh in the Reformation for both Protestants and Catholics, with much to be condemned on both sides. It is very easy for tempers to be inflamed when convictions are deeply held, and it was a very violent time.
But I state again, the Catholic church does indeed teach that we are saved by grace alone, with our good works being the result. We are called to show charity to others at all times by the works we do as we become the hands and feet of Christ on this earth. Peace!