In a libel case, should I ask the publisher of the statement what facts she relied on in deposition or via interrogatory? I'm concerned that since an interrogatory can be supplemented, that her answers could shift as the litigation progresses. While depositions bring the risk of an "I don't recall" answer.
should I ask the publisher of the statement what facts she relied on in deposition or via interrogatory?
Short answer: Yes, and you do it through deposition, not through written interrogatories.
Long answer: That is one of the most elementary and obvious questions a defamation plaintiff should formulate. But follow-up questions are significantly more important because there is where a defamer is likelier to incur contradictions. Keep in mind that a defamer will hardly ever admit guilt, whence a plaintiff needs skill to evidence the defamer's liability.
Although you can expect the defendant to be coached by her lawyer toward deposition, there is only so much that either crook can foresee or predict as to what direction your questioning will take. No lawyer can spoon-feed his client on every imaginable question that is relevant to the case. In this regard, the limit is your abilities to plan your questions as well as to "think quick on your feet".
A defamer is allowed to answer evasively (saying "I don't know", "I don't recall", or the like) on written interrogatory, a deposition, or a trial. The difference is that in a written interrogatory the defamer's lawyer has (and will use) the perfect opportunity to fabricate any and all answers, thereby defeating the purpose of follow-up questions.
Whether the defendant's answers shift over the course of litigation, that should be the least of your concerns. In fact, the defendant's significant shift might result in the defendant's loss of credibility before the jury.
You did not specify your jurisdiction. If this is anywhere in the US, you might be interested in my briefs in upper courts (here, here, and here). These will acquaint you (as well as any other victims of defamation) with case law on defamation and discovery from various jurisdictions in the US. You are welcome to all other records of the case I have uploaded here, but the briefs in the MI Supreme Court as well as the SCOTUS (and to a great extent in the MI Court Of Appeals) are most concise, and they reflect more proficiency than what can be expected in a pro se litigant's initial motions.
This transcript of defendant's deposition might also be of your interest. You will notice the defamer answered "I don't know" and "I don't recall" to the point of sounding demented. Some inconsistencies of his malingered amnesia are highlighted in the aforementioned briefs. In that transcript, you will also notice his lawyer's misconduct during the defamer's deposition. This shows the importance for you to be prepared to withstand similar acts of heckling by these people who like to call themselves "attorneys in good standing".
Lastly, even if you manage to evidence the defamer's liability and yet the court denies justice, having (and publishing) that evidence is invaluable. Not only this will state the record straight regarding your reputation, but others will be grateful for having verifiable information that will alert them about a defamer who might target them in the future.
Some "contributors" here will predictably downvote this answer (just like your question) under the false excuse of being "legal advice". Regardless, hopefully the material provided herein helps you get started on your quest to learn about the law.