An easy way to expand your conflict resolution ability is to begin using the two step discussion process. This is so simple that you might say, "Isn't it obvious?" Well, no. It certainly wasn't to me for many years. So here's a personal story that shows its power.
In a large institution where I worked, people rolled their eyes about the facilities manager. Kathy had been there for ages and people said she was an inflexible nitpicker. Everyone had a story - we all had to go through her to arrange space and technical support for our meetings and workshops.
Soon after I arrived, I too had my moment with Kathy. I needed access to meeting rooms at unusual hours. This required a special key - which she tightly controlled. I also needed her permission to bring in special equipment.