I agree that you have to trust your W to make the right choice and hopefully she will only introduce the children to someone who is safe. I have also heard of spouses giving the other spouse a heads up to let them know they will be introducing the children. My D's are 8 and 6........I have really struggled with this myself over the past couple months accepting that eventually they might be introduced to another man. I still struggle with how I will react/handle.
