Well number one there should never be a situation where either of you feel you are being picked over children. My husband married me with 3 children, he had none. My promise to him when we married was this: as long as you treat my children with respect, kindness, and are good to them I will never pick my child over you because I would see no reason to ever have to. He has never given me reason to do that ever.
If he and I disagreed with a decsion one or the other had made we would never discuss it in front of the children.
Then the next agreement was that once we both talked in private about the decsion and made a decsion together the person that made the decsion in front of the children was the one that, if the decsion had to be recalled was the one that delivered the message to the children.
That way there was no disrespect lost for that person.
That has worked great for us and we learned to commuicate very well with each other. It actually helped us out in the long run as well.
Now about the "B" thing. There is always two sides to every story but, I can't imagine ever getting to the point with the person you are married and in love with that you call each other such low and discusting names. Lots of lost respect happens there and it takes a long time to get that back.