I am designing a little device to measure some temps and the voltage in my car when it occurred to me that it wont be such a bad idea to also measure the charging current from the alternator.
What is it you really want to measure? Is it the charge current or the current from the alternator (alternator output current)?
The two currents are not the same, the alternator output feeds the car's electrical loads AND charges the battery.
If it's charge current, the measuring device needs to be located between the positive battery terminal and the vehicles main power bus, if it's alternator output current, the measuring device needs to be located between the alternator and it's connection to the vehicle's main bus.
There's very little reason to constantly monitor either current - the charge current is going to spike to 50~80% of the alternator capacity for the first minute or two after the engine is started and then gradually drop to a minimal current, the alternator output will constantly vary as the loads change - turn signals flashing will cause a variation, as will stepping on the brake - the variations will be so frequent and so minor that they would be a distraction whilst driving.