the only way to move on is to forgive him and not to mention about the affair anymore. it's good that he has shown some good improvement, this shows that he still loves you. guys will change if they have realised their mistake so no points in blaming or start an argumement, the best is to talk and find way out of it. the key to good relationship is communication, one have to listen before making a decision.
ya, sometimes it's difficult to forget but somehow you have to let go of the fear. try to focus on doing something that can distract you, talk to your friends, kids or go out even for a window shopping.
when i came to such situation like yours, will try to go out or meet up wt my friends or family. as for me husband always outstation for months or even years so i have to build a trust in him. we try to be open and honest about the relationship like who is our friends etc. i also know that he has a lot of female friends thru work but i dont't let this bother me so much. we have discuss about this before our marriage so i always take every step as a challenge. i'm lucky that my husband is not the jelousy type of guy so we dont't quarrel even when i'm out wt my male friend. when i suspicious of him, i will talk to him and let him explain before i make decision. i think it's best to listen to our husband rather than outsider coz we know actually what's happening unless we caught them red handed.