Well to be fair to Mr Sanford (welcome to FR Congressman!) these allegations do seem to all stem from his ex. And from what I hear, such proceedings can get quite nasty.
It may sound "nasty", but trying to shield children from abuse is frequently a very nasty business; most substance abuse is characterized by denial on the part of the abuser and the spouse being emotionally blackmailed into enabling the abuse or else being cast as the "cause" of the substance abuse -- but substance abusers must take responsibility for their own choices. If Mrs. Sanford were abusing drugs or alcohol, wouldn't her husband be justified in bringing it to the court's attention? The alternative is leaving the child in jeopardy and eroding the non-abusing spouse's position as a protector of the child, should something happen like a drunken car accident the other partner should have tried to help prevent by disclosing the abuse.
Neither a husband nor a wife can just waltz into a divorce court and rely upon their own say-so, especially in high-profile cases. There must be proof of some kind; whether it is the child testifying to witnessing drinking behavior (I think their youngest is a preteen or young teen), or the child's therapist testifying, or a police report of DUI, or another witness. Mrs. Sanford is an educated and competent woman and I doubt she would even try to make a claim that could be easily overturned. Remember there is a child caught in this crossfire. It is typical for most adults to take the side of the accused substance abuser over the potential harm to the child if this behavior is taking place in front of the child.