High-side current sensing with a rail-bound instrumentation amplifier?
A better way is to use a rail-to-rail input precision op-amp and a transistor. 







simulate this circuit &ndash; Schematic created using CircuitLab

Do an error budget calculation on your proposed homemade differential amplifier and I think you will find that 'Oh, that way madness lies'. The circuit above requires no matched parts. Voltage across R1 is 10mV/A and across R3 it is 1V/A. A MOSFET or Darlington can be used instead of Q1 for a bit better ideal accuracy. The main limits on accuracy are the tolerance of the resistors and the offset voltage of the op-amp. A 1% error in any  resistor results in a 1% error in the output. A 10uV offset voltage represents a 1mA error in the output. 

Suppose we divide down the 12V to 6V on each input. We still have the same sensitivity to R1, but a 1% error in one of the four resistors will cause an error of 30mV at the input to the in-amp. That's equivalent to a 60mV error at R1, which is an error of 6A! 

Yes, you could trim the resistors to get rid of most of the error for a while at one temperature but they would quickly drift out of spec. Even $25 0.01% resistors would not yield as good and stable a result as the 0.1 cent 1% resistors. That.. is engineering.