Q:

How do I prove to my physics teacher that adding a battery in parallel doesn't double the current?

simulate this circuit – Schematic created using CircuitLab
My physics teacher said that the current through the resistor is 4A because each battery has a current of 2A if hooked up to the resistor on its own, and so they both have 2A of current through them so the resistor has 4A total through it because of the junction rule (this was the explanation she gave when I asked her why the total current wasn't 2A), however that isn't true because the current through the resistor is 2A when the voltage is 80 (these batteries are in parallel), and so there is 1A through each battery. How should I explain that her logic doesn't work, as current does not double when you add another battery?
Edit:
Her response to me when I asked about ohm's law: each battery provides 2A of current on its own, so they combine because apparently, you can treat each loop separately, so then by the junction rule, the 2A currents join to become 4A.

A:

Just ask her what the voltage across the resistor is

A:

Method 1

simulate this circuit – Schematic created using CircuitLab
Figure 1. A simple practical experiment.
Performing an experiment with the circuit of Figure 1 would demonstrate that parallel voltage sources don't change the current. You should get a reading of 9 mA with either or both batteries in circuit.
Method 2
A thought experiment:

simulate this circuit
Figure 2. The battery box has two batteries and a switch whose position can't be seen.

What is the terminal voltage where the wires leave the box?
Does it change if I close the switch?
What is the expected current for that voltage?

A:

He said that

each battery has a current of 2A if hooked up to the resistor on its own, and so they both have 2A of current through them

Right. Both circuits have 2A through them.

simulate this circuit – Schematic created using CircuitLab

so the resistor has 4A total through it because of the junction rule

But if we combine the above circuits into one, we get this instead of the original circuit.

simulate this circuit
Both resistors having 2A throught them, 4A in total.
Update: Of course you can not just take two independent circuits, wire them together any way you like, and expect that they work the same afterwards. But it won't change a thing if you connect some points that are on the same potential.
Now, a basic question. What is the resultant resistance of the parallel connected R1=40Ω and R2=40Ω resistors?

 20Ω, because \$\dfrac{1}{\dfrac{1}{40}+\dfrac{1}{40}}=20\$

therefore the equivalent circuit is rather

simulate this circuit

