If a person’s initial motivation is to be free of unhealthy anger, is this motivation wrong? I ask because if forgiveness is a virtue, then it should be for the one who acted badly.

You are correct that as a virtue, forgiveness needs to be for the other.  Yet, it takes time to develop a motivation of goodwill toward someone who was cruel.  There is nothing dishonorable about having, as one’s initial motivation, a desire for self-preservation.  To use a physical analogy, if your knee is hurting, is it selfish to seek medical help?  If our heart is broken, is it selfish to try to mend that broken heart?  An initial focus on self that changes to a concern for the other is a typical pathway for growing in the virtue of forgiveness.

Have I truly forgiven if, whenever I am in the presence of the one who hurt me, I feel pain? I do wish the person well, but when I see him, the pain returns.

There is a difference between pain and unhealthy anger in which you hope that the other suffers.  You say that you wish him well and this is an important part of the forgiveness process.  Please keep in mind that within psychology we have a term called classical conditioning. In classical conditioning, over time we learn to associate certain people or situations with certain emotions.  A mother upon holding her baby feels love.  Classical conditioning links the sight or thought of the baby with love.  In your case, you have linked the person with pain.  You are classically conditioned to this link.  As you try to associate this person who hurt you with wishing him well, a new link will forge—–seeing him and wishing him well.  Be gentle with yourself on this.  Classical conditioning links (such as pain and seeing the one who caused the pain) take time to dissolve.

I have been hurt over and over again by a particular person and I want to forgive her. Is it better first if I get rid of my frustration and anger before I forgive?

Let us distinguish between healthy and unhealthy anger.  By healthy anger I mean the short-term feeling and expression of discontent over an injustice.  We all get angry or sad or disrupted in some way when people are very unjust to us.  Such healthy anger shows that we see ourselves as people who should be treated with respect.  It is good first to allow yourself this period of experiencing healthy anger before you start the forgiveness process.  In contrast, unhealthy anger is a deep feeling of resentment that does not easily go away.  It disrupts one’s concentration and energy.  You do not want to wait until the unhealthy anger fades because, quite frankly, if you were treated with great unfairness, then it is not likely to fade without going through the forgiveness process.  In sum, first allow a period of healthy anger.  Start forgiving to reduce or even eliminate unhealthy anger.

I am trying to forgive a family member who has what I would call “anger issues.” Is the forgiveness process different when you are forgiving someone who does not have anger issues compared with someone who has those issues?

I do think it may be more difficult to forgive someone who has what you call “anger issues” and then expresses that anger consistently to you.  You may have to forgive on a daily basis if you are in regular contact with a person who is continuously angry.  After you have forgiven to a deep enough level so that you can approach, in a civil way, this person, then it may be time to gently ask for justice.  Part of justice is to ask this person, if you feel safe with this, to begin working on the anger so that you are not hurt by it.

My ex-boyfriend no longer is my ex-boyfriend. We are back together, but I just cannot trust him. Have I truly reconciled if I cannot trust?

Being together does not necessarily mean that you are reconciled.  Reconciliation includes trust, but trust is earned back inch-by-inch. Does your boyfriend show you signs that he has remorse (sadness for what he did)?  Does he show repentance (saying he is sorry)?  Does he engage in recompense (behaviorally trying to make up for what he did and behaviorally showing he is trustworthy)?  Keep these three issues in mind (remorse, repentance, and recompense) as a way to build your trust so that you can achieve a true reconciliation.