MOSFET Triggers with Electrostatic Energy
I would recommend connecting R2 on the other side of R3 closer to the gate of the MOSFET. Your schematic also suggests that the pull-down resistor uses a different ground to the source of the MOSFET (GND and GNDA respectively); i would connecting the pull-down resistor as close a possible to the MOSFET between the gate and source terminals.

If you still have problems then, since you're driving something slow like a mechanical relay, you can add some capacitance between the gate and the source of the MOSFET so that more charge is required to raise the gate-source voltage to the threshold level. An alternative to this is to add a Schottky diode in parallel with R3 to give a low impedance pull-down path when the MOSFET is blocking. Vgs(th) for the MOSFET is quoted at 1 V so you don't need to use a Schottky diode but it'll give the solutiuon the best chance of working for you.