Measuring continuous voltage and current circuit
It's not a problem, it's the way the circuit works. Keep in mind that, when operating properly with negative feedback, the + and - inputs are essentially at the same voltage.

Now, once your "DAC" produces a voltage V, the same voltage V appears on R4. Since the current through the FET and R4 is the same, the power dissipated in R4 will be proportional to V, while the power dissipated in the FET will be proportional to (V+ - 4), and for V much smaller than V+ the power dissipated in the FET will be larger than the power dissipated in R4.

Your attempt to parallel 2 FETs was not horribly wrong, but different FETs have different gains for the same gate voltage, so one of the FETs is hogging most of the current, but in effect the gain of the composite FET varies with gate voltage, since if one FET is on and the gate voltage rises above the turn-on threshold for the other the amount of current will increase dramatically. This gain nonlinearity, combined with the capacitive loading on the op amp due to gate capacitance, is causing your op amp to become at least slightly unstable. This is made worse by high-frequency components of your PWM getting past the cap.

You are best off sticking with one FET, and putting a heatsink on it. You should also check the voltage across R4, and make sure that your op amp/FET is not oscillating, which will draw significantly more power than if it is well-behaved.