But since you are using GPIO2, the above won't work due to boot process, you will need a second stage MOSFET to invert the logic, because GPIO2 need to be pulled up.
So, with 2 MOSFET, it should look something similar to that, except that T2 would be a MOSFET and the GPIO2 Pullup is not shown here :
I tried to give a break down of what I thought the first schematic was but didn't get a reply so I am still unsure of what I am looking at.
There is no Arduino out on my circuit, I am guessing that this the GPIO2 pin ?
From there a 1k resistor into the middle leg of the first mosfet?
The right leg to ground?
Left leg to a 10K resistor then what is the 12V?
Also left leg to the 2nd mosfet? It looks like this connection goes to all legs of the 2nd mosfet?
The left leg of second mosfet to the relay and the right to ground?
Sorry if this is a bit of a pain but I am trying to understand what I am seeing.
So, No, the right pins (Drain) should not be connected to GND, it should be the left pins (Source).
(so, maybe that was your wiring problem)
The R2 on previous schematic is not needed with MOSFET (it was there only in the case of a NPN transistor), so the gate can be connected to GPIO2 directly as long as you have the PullUp for boot process (not shown here).