Replacing a switch with MOSFETs
Why not use two devices then each can be powered by their individual local battery supply.

If not then TI have a range of power/load switches that may be suitable. I'm thinking of the TPS2080 listed on this page amongst other devices that may also be suitable. The TPS2080 is a dual supply with &lt;0.1 ohms on resistance and supports a change over contact. It has a built-in charge pump that should overcome the problem you have.

If all else fails then create a low power "higher" voltage rail and use this for the chip supply.