Mighty - most of here are fixers. There are good reasons why this is so!
I still have to stop myself trying to fix things between my xh and our adult children. With other people I am getting much better.
Nothing you can do will fix him, but cake eating is not healthy for either of you. He may well go back to blaming you. Do not take this personally as it is mostly self protective projection on his part.
If he wants to see the children he needs to make the arrangements. Only you can decide if he is welcome in your home or not. But, absolutely no coming and going without a clear arrangement.
And Job is right, if they come back too soon they almost always run again at some point.
I very am sorry the child is his, but there was always the possibility it could be. I wouldn't like to have a relationship with someone who doubted the paternity of his child. Just sayin'.
