You have already answered your own question in your question. You want to be with her, which means she is worth forgiving. You can be mad and share that with her, and help her understand things that upset you. But also be forgiving because we all make mistakes and we heal through forgiveness. If it were you who made the mistake, what would you hope for her to do? What fear do you have around forgiving her, that it might happen again? That she doesn't love you? If you know that she loves you, and you share this experience together, you can support eachother through the pain of it and become closer because of that. But both parties need to be willing to support one another. So this is your chance to find out if she wants to be with you as much as you do with her.