OK, when you're taking measurements of voltage drop on shunt resistor between Source and minus you have to observe several parameters:

1. Ground clip of your probe must be on minus and active end on Source. Between them is shunt resistor. Don't connect other DSO probe to any point.
2. Shunt shouldn't be inductive. For the current ranges you're measuring you need shunt of 0.1 Ohm (you will see 1V for every 10 amperes). Don't go for higher shunt values because it will probably heat up quickly. If the shunt resistance is too high it's resistance will impede current flow. If the shunt resistance is too low the voltage drop will be too low to precisely measure.
3. You need to know shunt resistance or you cannot calculate anything. You can use ampermeter and it's shunt resistance. Usually there is a value of shunt stated somewhere on the casing ampermeter or inside of it.

If you don't know shunt resistance of your ampermeter simply take adjustable DC voltage source and set it's voltage until you get ampermeter reading (in short circuit) of some known current value (let's say 1A or some other round number). Connect DSO probe in parallel with ampermeter shunt. Now you have current value (ampermeter reading) and voltage drop on shunt (DSO reading). Use Ohm's law to calculate resistance of shunt.

Now that you know shunt value you can measure RMS voltage directly with oscilloscope and use that value to calculate RMS current value. And again since we're dealing with pulsed DC and introducing noise you must observe that shunt resistor is non-inductive. Dedicated, calibrated shunt would be ideal if you can get one (it's not so expensive) but measurements with this configuration should also serve as well.