Okay. First of all, using a mobile phone whilst driving is stupid. That isn't debatable and he's a naughty boy. Maybe that could be discussed in another thread, it's not relevent here at all. Neither is your opinion of whether this guy is a good father or person, I've not seen anything here to make a definitive call.
The goading of Carragher is mild to say the least. He will have experienced much worse throughout his career and it's the inevitable price you pay for having the best job in the world for which you are rewarded handsomely. From Fergie being punched in the balls to Gary Neville having his car tipped over at some red lights, it's part and parcel of being part of the game.
In this case, the 'abuse' isn't even an issue. Shouting "2-1" at someone isn't offensive. At all. You're in a Range Rover with an incredible sound system and windows, this is easy to ignore. Having a short fuse is one thing, spitting at a 14-year old girl is another. This is very bad. The goading here does not equal the reaction. He's a professional and knows better. Whatever happens, he can have no complaints.