He can apply to the court for an order which he considers to be in the best interests of the children. He may argue that the children shouldn't come into contact with you because you are new on the scene and because you have a criminal record. However it is very unlikely that the court would stop her seeing her own children because of you. Happy to discuss further. I hope that helps. Please leave a positive rating so that I am credited for my time.
Thanks and sorry, I see your follow up question now. The adultery would not be taken into account by the court unless in some way it affected the welfare of the children such as you having an affair in the presence of the children where they might be upset to give an example. Hope that helps.