Arduino and N mosfet lithium battery charging/discharging measuring capacity
Surely a high side PFET connecting the battery + terminal to the 4.2V external supply is enough. I hope you aren't doing anything unsafe, I really hope you've read about thermal issues, charge currents and voltage cycles with Lipo batties. 

If you have the default logic state as the 4.2V thing connected to the battery, then have the system with a pull down resistor on Pin 12. Then when Pin 12 goes high, it will turn on the NFET low-side switch to provide the 2 Ohm load, and the gate voltage of the P fet will rise and turn it off, thus allowing you to test the battery without the 4.2V thing interfering. 

You can swap the logic (not recommended, unless you also detach the battery when not in use) by putting a pull-up resistor on Pin 12 and driving it low to allow the battery to charge again.