My advice is don't bother with a voltage regulator IC. Make your own using a transistor and an op-amp.
How much voltage are you planning to drop across the low current shunt? Unless it's considerable, say >1mV per μA, the arrangement you've posted is unlikely to work well, due to the mismatch in resistors and op-amp offset voltages.
How much voltage headroom is there?
I think you should use a relatively high value resistor for the low current shunt, say 1k, and bypass it when it's not being used. Three separate shunts for different ranges would probably be ideal: 1k for under 200μA, 2R for up to 100mA and 100mOhm for up to 2A. There would be no point in disconnecting any of the shunts: keep the 1k and 2R in place when measuring 2A, just connect the 100mR shunt in parallel: the other resistors are so high value, it will make little difference, which could even be calibrated out, if necessary.
Some kind of switch would need to be used to select the appropriate shunt: relays have a very low resistance, but are slow, a MOSFET would be ideal, but has a much higher resistance and both P and N channel devices may be required, to make a simple analogue switch, unless there's plenty of voltage headroom.