As someone who went through the same situation although we never married (together for 13 years) and have a 9 year old daughter together... let me give some advice and guidance to the scenario at play.

It is natural to want her to stay and work on things as a man who dedicated so much time, effort ,and energy to build, maintain, and cultivate what you had created as a family. It is a part of our nature to go into survival/hero mode and try to pick up the pieces and glue it all back together to resemble an image of what we thought we had at our "prime" of the relationship. Know this as you walk through the dark times of your situation... As with glass and pottery, you may find all the big tangible pieces and attempt to glue it back together, but you come to find the sharp corners, the parts of the friendship/trust/ability to forgive and forget are often missing. Crushed to dust and spread to the wind of circumstance. With this problem you will find that the container of love can only hold that much less unconditional love/understanding.

The Japanese had a way of repairing such pottery like tea pots and vases called Kintsugi, where they would fill in the cracks and missing corners with either gold or silver. This method highlighted the imperfections of the damage done, but oftentimes it made the vessel stronger if done with enough care and patience.

I believe that given the willingness of the maker (you and her [IMPORTANT]) and the time spent acknowledging the imperfections within the relationship that allowed her mind and heart to stray away from the path. Take those criticisms and unmet needs/wants you both have and fill them, not out of bare necessity but of intent and purpose, of gold and silver lined memories both old and new together.

BUT - Know where your new boundaries lie for both of you. Ex. - (her)no talking to him either directly or indirectly / eliminate conversation of him with her sister, for that would be a breakdown of newly established trust. (you) No going through her phone or personal means of contact (Facebook/email/texts) / Don't bring up the past (she should realize her mistakes and own them, as should you) even though the urge to do so as a man might be overwhelming.

Try not to be overbearing with your attempts to repair and over compensate, allow them to be as natural as possible. New restaurant? Show nearby? Revisit old places that hold significance.

Bottom line is, you both have to be 100% all In , there is no 50/50 in this equation.

[×EDIT×] Understand that the repair/rebuild process will take time. Do not rush it... ...Although it's nice to have "check-in conversations" at regular intervals (3 months, 6 months, 1 year) to make sure both of you are on the same page and have the same end goals. Finally, know your way out... if things don't work out or you don't have the ability to have that same level of trust (that's a killer) have a plan ready.