Slander

It sounds as if you already have an attorney, so I'd rely on their thoughts over mine, by a mile, as they know the details of the whole picture.

But, here's some thoughts:
1) If there was a slander, unlike with most injuries in Texas, the statute of limitations will be only one year; and
2) For most statements made in the formal context of discovery, slander will not apply. Usually, the law suit is a free-speech zone. What you may want to explore would include: (a) who told them Mom had a drug problem; and (b) did anybody say so outside of the formal communications of the suit.

Most courts will give great leeway to an attorney in the way he is pursuing discovery. He would probably get by to say that he had heard that mother had an addiction and was pursuing information about it. Your attorney could file a motion for sanctions or discovery abuse or you could file a grievance with the Office of Chief Disciplainary Counsel with the State Bar of Texas(www.texasbar.com). But the reality of pursuing a libel lawsuit is very remote.

Mr. Bennet's answer pretty much sums up the law here in Texas sa it relates to defamation made in the course of litigation proceedings. Your attorney could seek Rule 13 sanctions if the ocnduct is egregious enough.

The other attorneys have provided good substantive background in their answers, but I would also point out that sometimes attorneys make mistake and use forms from one case to another. While I don't know the specifics of your situation, it may be possible that the attorney simply used a form and the question was asked inadvertently. I regularly receive form discovery requests from other attorneys, and sometimes questions are asked that have nothing to do with the case. I usually pick up the phone and call the attorney to verify if he/she actually intended to ask the specific question. Sometimes the answer is yes (for reasons of their own), but sometimes the answer is no. Just a thought!