Accepting other people apology is very hard. We usually don't accept the apology in our brain and never forgive the person from our heart. This is very natural. Even if the person got punishment for what he did, even if he died; we don't forgive them. One of the reasons of this is, we don't learn to forgive culturally and we don't teach ourselves also to forgive.
Holding the emotion could never be the solution. We didn't learn to accept that it's okay to make mistakes, it's okay as we are human. Rather, we learn and also teach others to toggle with different emotions which lets us not accept an apology. And I'm not only talking about forgiving others, but we also have to learn to forgive us too.
A human being doesn't need to be taught to forgive; one needs only find what one needs to learn. This means that when one has a strong feeling that something is wrong, just don't wait until later. The more times you wait until later, the weaker your feeling becomes. The feeling remains, but later you feel weaker. That is, in one case, you wait until you get the sense that it won't be much of an offense in the future; in the other, you wait until you find the right moment.
One of the basic things we can do to learn forgiveness is to Reconnect with the spirit. Make a settlement with your brain that you are accepting the apology for this this and this. Stay connected with the moment, don't try to forget it rather forgive it. Turn yourself towards the fact that you have to forgive to live a better life. If you believe in God, you can turn it to that sprit also. It helps and it always will help to flourish our presence rather holding the emotions.
Accepting our emotions is necessary. I'm not saying we need not show anger who did very wrong to us. But if the person requests an apology, I believe that there's no necessity to hold the emotions anymore. Yeah, it's hard if it's very personal. I say, call for punishment and what makes you feel better. But in your heart accept their apology and give your mind the feeling of peace and freedom from certain emotions.