Upon request, I would like to take the topic of forgiveness and discuss my views on how to confront a situation where you want to forgive someone after a conflict but they either will not accept your forgiveness/apology or they will not apologize to you for their wrongdoing. Although it should be mentioned first and foremost that every scenario is different and there may be variables present that change the circumstances on a normal basis, this is the basic path I use when I find myself in these situations.
To begin with, I think it is important to place yourself in their shoes and try to understand why the other person or group is acting the way they are. This can be done in a number of ways. Although self reflection is probably the easiest route, there are also more chances of you missing a piece of the puzzle that could be very important to the other person. I have found it useful to confront the person face to face in a good way and try to talk things out. If this process is easier said than done, it might be wise to bring in a professional who can mediate the conversation. With this being said, it is also important to have the professional be as neutral as possible and to hold the conversation in a neutral setting so no member is given an advantage. By understanding the person on a deeper level, it is possible to understand what may be upsetting them and both parties will be closer to finding a common ground as well as a way to fix the problem.
If this action is taken and the other person still does not accept your apology, it may be necessary to allow some time to pass. Some people work longer than others to understand the different levels of an issue and if one member is trying to fix everything as fast as possible, they may not feel like they are being heard in the situation. Although I would not suggest this being the first method of communication, sometimes it is beneficial to write the other person a letter explaining how you see the situation, how you think they see the situation and how you plan to resolve things. Being the person seeking forgiveness, it is important to use "I statements" such as "I feel this or I feel that." By using this as well as facts to back up your view on things, it is easier to take away assumptions and move into the meat of the problem. Also by using "I feel" statements, the other person cannot argue with the way that you feel.
I know this is not the most preferred response, but sometimes things don't work out in the end. Maybe there is a piece of the puzzle that you will never know or things just don't go to plan. In these cases, all you can do is take control of your own pieces. Try to clean up any things on your side and place the forgiving part on them. Maybe they will eventually forgive you and maybe they won't, but in the end you did all that you could do in the situation. With the fun of free will, you will never have control of anyone except for yourself. Sometimes this means you need to take control of the situation and be the bigger person by taking the blame off someone else and apologizing for things you didn't do. It is not the most admirable job, but a leader is someone who resolves conflict and sometimes takes the conflict upon themselves in order to save a relationship because they are strong individuals who believe a team or relationship is more important than a grudge. I do not want to sound like a broken record on this concept, but always remember positive interactions will always get you further in life than negative relationships. Take the higher rode, forgive the unforgivable, and move on with your life. You only live life once, there is really no point in getting stressed over a bad relationship for longer than it needs to be.