(micro) SD Card with two Masters

I'm currently working on a project where I need to read an sd card from two different masters (computer/arduino) not at the same time but I don't want to disconnect and reconnect. In other words the sd card is inserted in the arduino and without physically moving the sd card I want to read the files on another arduino/computer/etc.

===========>Arduino 1
SD CARD ======{
===========>Arduino 2

You need a chip like this

I keep meaning to make shield for this, with some mux control on the SD control lines so arduino could control the card too.