Forgiveness happens inside of you. You can forgive someone all by yourself, with no involvement at all required from the person you are forgiving. We all must forgive because it is through forgiveness that we let go of anger, pain, resentment, and other negative feelings towards another person which are eating us alive. So we forgive first of all for our own sake, and only secondarily for the sake of the person we are forgiving. Reconciliation, however, is a two-way street. You cannot be reconciled to someone who does not wish to be reconciled to you. And the fact that someone seeks reconciliation with you does not mean you must permit it.
This means that forgiveness sometimes must occur without reconciliation. If someone has wronged you deeply and insists on reconciliation with you even though they have never admitted to their wrongdoing, reconciliation will be nearly impossible. You can forgive them and wish them well, but still refuse to be reconciled. After all, a person who will not admit to having harmed you is quite likely to harm you again and you do not have to expose yourself to this. It is critical for you to forgive, but you are not obligated to reconcile.
In writing this I am not minimizing reconciliation. It is always important to reconcile wherever possible. But reconciliation involves two parties, admission of wrongdoing, the seeking and granting of forgiveness, and a promise from the wrongdoer not to repeat the offense. Any wrongdoer who demands reconciliation but seeks to short-circuit this process is asking more than they have a right to ask. If, as wrongdoers often do, they use God and religion to guilt-trip you into reconciling without them accepting responsibility, then they are even more deeply broken than you had realized. Forgive. Let go of anger and resentment in your heart. Then draw your boundaries and lovingly stand firm.