Switch a differential I²C bus section, controlled via I²C
There are quite a few differential buses and their characteristics define possible switching methods. What transceivers do you use?

Regardless of the above, I think you are fighting windmills here.


Even though differential buses generally capable of faster speeds, in your case they are limited by original I2C speed. Converting to I2C and back at the MUX does not introduce any delays.
You want to use I2C to control the switch. This is fine. But if your bus is not something I2C device can be connected to then you have to convert it to I2C anyway, so that your message would be understood. And if you already converted it, why not convert MUX outputs again?
Most of the analog switches have tri-stated outputs. So they can only be used with differential buses that support biasing, to avoid erroneous signals on disconnected segments. This is something that pure I2C MUX does for you automatically.


There are 2 and 8 channel switches like TCA954*A series, that are electrically capable of switching some of the differential buses. The problem is that their own I2C inputs internally connected to same wires.

There are I2C controlled analog switches, like ADG715, MAX4572, and some even designed for differential signals, like LTC1393. Once again, you still have to convert differential to I2C in order to control that switch.

When I look at possible SDA/SCL combinations and transitions, I don't see anything that might affect either disconnected or new bus segment. The only exception is that old bus segment might miss stop condition. However, since last command on that bus was addressed to the switch itself, it doesn't really matter. The new bus segment might receive start condition and ACK as first bit, but it will be followed by stop condition anyway, so no problem here as well.

But you have to figure out first if that is what you really need. Otherwise you might end up with much more cumbersome schematics than simple translation to I2C and back at the MUX.

UPDATE

Here is final analog switch solution: Use either MAX4562 on SDA line only or MAX4572 on both SDA and SCL. Your differential segments connected to outputs must be failsafe biased to ensure they translated into idle I2C state when segment disconnected from bus.

UPDATE 2

Since you are using dI2C it already requires termination with biasing, so a good fit for analog switch, which can be used to disconnect SDA or SCL or both. As I mentioned above, this will create several racing situations resulting in slaves on disconnected segment receiving either string of start-stop conditions or continuous stream of "1" bits. While neither of these should result in unexpected actions by slaves, it is not a clean design.

So, I am standing behind my initial assessment that using normal I2C switch and two differential transceivers before and after it would be most robust solution.