I have personally found the Internal Family Systems Psycological model and similar models that work with "Parts" very helpful to understand this.

DBT helped me tremendously. As you described, you have an emotional and rational mindset in which you "react" to a situation. With DBT, you can learn to utilize both together, which is called a wise (or reasonable) mindset in which you can "respond" to a situation. You can learn to recognize how you initially think/react to a situation. Then, when not in that situation, you can think things through, write down the emotional (i am responsible for their problems) and rational (I don't have anything to do with their problems) reactions down. Think of a way to compromise those reactions into a reasonable (or wise) response (I am not responsible for their problems, but I can sympathize with them). Make a plan of how you can you can respond in a wise/reasonable mindset next time. I use the word "react" for emotional and rational mindset because they are usually automatic and not well thought through. I use the word "respond" for wise mind because it is a predetermined or thought-out response. I hope this helps in some way. Using DBT kept me from completely losing my mind during a really tough time, where my patience and understanding were very thin. If you would like to know more about DBT, check out dbtselfhelp.com.