I understand you will be in deep pain n want to bring this man n loving time back in life but as you have described its not possible in given circumstances n any efforts from your side will bring more pain to you and the other person. It will be very difficult for you to see your lover with some other women but you need to accept the reality.
Please don’t get involve in any relationship immediately.
Give yourself time to heal this wound.
Take care of yourself n know very well this phase will be over n you will be happy again in life. Connect to your old good friends n spend time doing what you really enjoy…like dancing, writing, watching movies, taking your daughter to park.
You priority needs to be to put energy in your health n happiness not in pulling other girl down n bringing pain in her life. It will only make situation worse. Let go him with understanding and trust in universe. You are taken care n will lead a beautiful life.
With warm hug n love.