As long as the in-amp doesn't affect the current through the resistor or the voltage at either of its terminals, there shouldn't be any issue here.
However, the INA180 will affect those things. Its non-inverting input is a resistive path to ground, and its inverting input is a resistive path to the voltage of its inverting input (for inputs and outputs within its bandwidth and IO voltage range) or a complex impedance to ground (for inputs and outputs outside its bandwidth or IO voltage range). The INA138 has different particulars, but a similar result. It's up to you whether the inaccuracy and potential instability this can cause is tolerable for your application. I'd be concerned about out-of-bandwidth issues, personally. (Out-of-range issues can be mitigated by appropriate choice of gain and sense resistor.)
You could use an in-amp with a higher input impedance, though you'd probably require a power supply for it higher than V_BATT. It should be practical to generate this with a small charge pump; one amplifier won't need much current. The INA823, for instance, might work.
It would be best to use a power switch device that has a built-in current sense output, like a TPS4811 or TPS2640. It doesn't appear, on a cursory search, that there are any options for dual-channel ones that work to as high a voltage as you need, but two single-channel ones should do the job as well.
