Stubborn, grudge holding, process to forgive is slow

I come from a long line of strong, opinionated, stubborn people who are eager to prove others wrong. My people hold on to grudges and are slow to let go. We love to argue and prove the other person wrong. Here is an example that I have heard my whole life. My great grandparents came from Greece when my grandpa was super young. They were excited to start over in America. From what I've been told, America did not recognize their training/schooling, so they could not get jobs in their chosen fields. So being the proud, stubborn people that they were, they became angry and refused to learn English. They Forbide English to be spoken in their homes for the rest of their lives.

I have a brother who hates peppers. He is growing ghost peppers, not to eat, but to prove he can. Ghost Peppers are suppose to be super hard to grow. He wanted to prove that they are easy to grow. So he is growing them even though he will never eat them. 

These are just two examples of my family's stubbornness. Stubbornness is not necessarily a bad thing. Being stubborn helps us to never give up despite the odds being negative. When stubbornness becomes a problem is when we refuse to let go and forgive others. I really struggle with forgiveness. 

How do you truly forgive someone when they don't apologize or even admit their wrongs or honestly believe they have not done you wrong? How do you forgive someone who keeps doing the action that you are trying to forgive them for? I want an apology before I forgive. But there are just some people in my life who will never apologize. I want a person to change their behavior before I forgive them. How can I forgive you for spreading lies about me when you continue to do so? It is extremely difficult to forgive in these cases. 

I keep being smacked in the face with these verses: Matthew 18:21-23 "Then Peter came to Jesus and asked, "Lord, how many times shall I forgive my brother or sister who sins against me? Up to seven times?" Jesus answered, "I tell you, not seven times, but seventy-seven times?" 

 This is the quote I have been trying to apply to my life. I truly believe when we hold on to that hurt and anger, refusing to forgive and let go, it causes us so much pain. I have done tons of reflection lately. I've realized part of my inability to forgive is my need for the sincere apology.  I just need to hear they were wrong, they are sorry, and they will not repeat the action. That is in a perfect world. 

What I'm realizing is I need to discover peace and forgiveness without those things. I am a work in process but I'm getting there. So I just keep repeating forgive, let go, move on.