From where I sit it boils down to a simple choice for Paul, does he want a life with Becs and his new baby or does he want to drink, that simple, choose one or the other, because cant have both.
Choosing the family life is hard, it will never be easy, every day will be a struggle and temptation will always be there, he will stumble and fall, but hopefully get back up and carry on.
However it seems he will choose the drink, because its easier, because he says he doesnt actually have a problem with it, because ultimately its what he wants and he is an addict even if he wont admit it to himself.
Its his life and only he can decide if he wants to fuck it up or not.