No contact is a tool for you. It is to help you heal, to give you space for yourself. It is not going to fix her or wake her up.
You do not have to wait for her to contact you, although that is probably a sound recommendation. While she is wrapped up in infatuation your words will have no meaning, you might as well save your breath. She needs to go through these feelings and grow. If and when you two do talk, be kind and friendly, short and to the point, businesslike. You are correct you two are not friends right now; your friends don’t treat you that way.
You need to become the best version of yourself. Do all that inner work, and find out who F really is. Find your headings and keep walking forward. Be a man she would be a fool to leave.
Time and space. She needs it. She will take it. So give it to her.
Her affair has to crash and burn, she needs to miss you, and then look within herself. Your best chance at helping her, and a reconciliation, is to focus on you and your kids and let her go, let her run. This is just a chance. However you will be better from all your efforts no matter what happens.
Focus on you and kids. Choose better not bitter.
How is your detachment coming along?
DnJ
Feelings are fleeting. Be better, not bitter. Love the person, forgive the sin.