So, you've taken care of the first step of apologizing and you definitely have a handle on the second. Without further adieu, here 's step 3 (which might just be the most important step): 3. Identify the main hurt in the other person.
Being "hurt" can mean a lot of different things. Knowing someone is hurt is a good start, but truly trying to understand the feelings at the core of the hurt makes a huge difference in helping the other person receive an apology.
When receiving an apology, it's very meaningful to see that the "apologizer" has taken the time to consider why X act was so hurtful. Identifying the main hurt helps the other person feel understood and validated.
People need to feel that their feelings are validated in order to move on.
It cannot be emphasized enough: if a person does not feel validated, they will never accept your apology. Let the hurt person know that you get how they feel and that it makes sense that they feel that way.
Here are a few 'main hurts' that people often experience when an apology is due, hopefully they can help you to identify, then validate the specific feelings at the heart of the issue:
Feeling left out/abandoned
Feeling that trust is irrevocably damaged
Feeling that they are not being taken seriously
Feeling that they are not cared about/thought of
Feeling that their ideas and/or wants are being dismissed
If it's not obvious to you why the person is so hurt, part of your apology can be starting a dialogue about it. "I obviously know you're hurt, but I really want to understand what about this bothered you the most. I want to make sure I completely understand how you feel/felt, could you please explain it to me?" Then just listen, listen, listen. Listening is the most simple form of compassion. Try not to ruin this opportunity to be compassionate by interrupting or defending yourself after the person is done speaking. Remember that you can't listen if you're talking, so zip it!
After you've identified the main hurt in another, you're ready for the next step, which is coming soon.