If you both are committed to creating a functional relationship, agree to start doing it today, without any judgments about the past. Be willing to work in the solution and let go of your need to control the outcome, moment to moment, one day at a time. Joy can only be experienced in the present moment. Most of our fears about what may happen in this relationship are really fears we experienced in past relationships, and have nothing to do with this person. Think about it.
Life is short.
Don't waste it on arguments that have no meaning or purpose. You can always agree to disagree if you need to. Then laugh about it and go on to the next thing. Start observing your arguing as just another one of our dysfunctional, immature habits that need to be broken. O.K. To error is human, and there is great virtue in all forgiveness, ourselves included.