premise: Your Honor, one thing I might ask, since it is perhaps likely that issues are going to arise during the deposition, I'm wondering if we could now attempt to schedule the deposition at a time when everybody, including Your Honor, might be available to intercede.
hypothesis: They want to have someone fill in for the judge during the deposition.
reason: They are saying that they want to deposition when the judge is AVAILABLE. They don't want someone to fill in... they make it clear that the judge needs to be available. So the statement that they would be happy with someone filling in is incorrect. 