Is it worth trying to save the marriage when the trust is no longer there or better to call it quits

I would want couples counseling in order to give this marriage another attempt. 

People cheat for different reasons. It can be anger-passive aggressive response, it can be the other cheated previously, it can be loneliness, it can be because they are brought up to not value monogamy. It sounds like the other individual is concerned about how adultery is going to affect the divorce, or they fully realized what it will mean to go through with the divorce. It means moving, financial changes, change in friendships. Divorce is often compared to a death in the family and when one finally realizes that, it can make them have a change of heart. Maybe they realized the "grass was not greener on the other side?" Maybe they realized that the children will be affected by it in ways they had not considered at first? Including pets...

How safe do you feel to continue the relationship with this person? Do you feel they can be reasonable and honestly look at what they have done and take responsibility for cheating? Can you also do the same- take responsibility for how you may have influenced certain situations as well?  It sounds like this partner did not put a lot of thought into their actions and was acting from a place of anger and hurt. You will need to address those feelings with them, and your own in therapy and decide whether you are both willing to be vulnerable again with each other and try to fix these problems together. It will take time and both of you will need to be committed to making changes and be able to take responsibility for your own actions. If one of you is not capable of recognizing your own mistakes, the changes you will make may not be enough to save the marriage, however it will give you clarity as to what when wrong in your marriage and how not to repeat the same mistakes in another relationship in the future.