There are two things that need to happen here.
1. Contact does need to be ended in a way that is satisfying for you.
2. You need to work on your marriage, so that the void your husband is feeling can be filled by you, and the marriage you create together on the other side of this mess is one where you are both happy and fulfilled.
ENDING EXTRAMARITAL AFFAIRS
When people end their affairs, they go through a grieving period. They often think they are/were in love with the other person. Really they were in love with the way they felt. It is the reflection of themselves in the affair partner’s eyes, which they love.
An affair is an escape from reality. The fantasy of an affair serves as a temporary numbing of pain we may have in our lives. Like being a drug addict or an alcoholic, once our “high” wears off we are left with even more pain, and added to it is the mess we’ve made of our lives.
Generally it takes 3 – 6 months for this grieving the loss of the affair period to pass. It’s similar to the period of time where an alcoholic is sobering up. Before they “thaw out”, they generally don’t think logically, they make a lot of mistakes, and often aren’t very nice. They don’t come on their knees begging forgiveness like one might expect. That comes later.
Contact with the 3rd party will only serve to feed the affair, and after renewed contact the “thawing out” period begins again. Your gut instinct is right in not risking your family’s wellbeing by agreeing to this attempt at closure, which more than likely will have the opposite effect.
People who are caught up in affair fantasyland have a very difficult time ending their affairs. Many want permission to end their affairs gradually. I have yet to work with a couple where this gradual ending of the affair approach ended in a restored marriage.
My own husband said that when I insisted he end his “friendship” (as he called it then) with the other woman, he felt like he was cutting his right hand off. That’s a pretty strong analogy. From those who have made it, we can assure you this is necessary. The “I’ll-quit-slowly” approach to ending affairs is not effective.