Driving two MOSFETs with one AND Gate?
You dont need R8, R9, R10 and R11... if you want a current limiting  resistor for the gate of each mosfet you can keep R10 and R11 in your design, depending on how fast you want this mosfet to turn on you might want a lower value for them, I think 100 ohms is okay for this application.

Second issue, I would add a driver IC between your gate and your MOSFETs, logic gates are not meant to provide driving currents, even though MOSFETs require small currents for their turn on(few mAs or so)  I would add a proper driver IC that takes the signal and can drive some current to the gate of your switch. a 5V  dual MOSFET driver IC or something alike will do the trick here proving current for both switches.

Third, seeing you current and voltages it seems your MOSFET will be  okay, but see what are the tradeoffs of getting a bigger one and having more leeway on that end