If your brother-in-law truly refuses to forgive you or have anything to do with you, then there really isn’t much more you can do–except to forgive him for his attitude and continue to pray for him.
At the same time, however, I can’t help but wonder if you realize just how deeply you have apparently hurt him. Although you don’t say what you did, clearly it caused your brother-in-law to lose trust in you, and you probably hurt him in other ways as well. One reason he may not be willing to forgive you is because he doesn’t think you take what you did seriously enough.
In other words, have you honestly sought to put yourself into his shoes, and tried to imagine how you would have reacted if he had treated you the way you treated him? The Bible says, “So in everything, do to others what you would have them do to you” (Matthew 7:12). Let your prayer be that of the psalmist: “Test me, O Lord, and try me, examine my heart and my mind” (Psalm 26:2).
Don’t give up. Keep praying that you will be reconciled, and let him know whenever you can (e.g., through letters or e-mails) how sorry you are for what you did. Most of all, seek God’s forgiveness for what you have done. Christ died to make your forgiveness possible; have you received Him into your life?