The sign of peace during the communion rite both recalls Jesus’ injunction to make peace with our brother or sister before bringing our gifts to the Lord (Matthew 5:23-24) and also our prayer for Christ’s peace and unity (Communion Rite, Roman Missal Third Edition). Sometimes the sign of peace celebrates forgiveness given and received; sometimes it expresses our hope for forgiveness and healing yet to come. If you are conscious of sin, it is important for you to express contrition before approaching for communion. But if someone has sinned against you, you do not necessarily have to specifically offer that person a sign of peace in order to receive communion. When deep hurt has been caused, forgiveness does not happen overnight. You need time to work through the pain surrounding your wife’s affair, and it is prudent to keep distance from this person until or unless you want to be in contact. Unless you live in an extremely small community that worships in exceptionally tight quarters, you can probably avoid greeting this person, especially during the sign of peace.
A larger question would be what if that person extends YOU a sign of peace? In that case accepting the gesture may be the first step in making amends with this person and beginning your own healing journey.

(Mike Hayes contributed to this answer).