In my ammended circuit (Post #18) you will see a 0.1uF cap (ceramic) connected across pins 1 and 2 on the MOSFET; you have omitted this in your 3 sims. The circuit should work once the cap is added.
Let me know how you get on.

 

The cap C2 is there
According to your post , pin 1 is going to ground
Pin 2 , is going to One side PB, and R3, and also to C2 ( just beside C1)
I tested with 0.01 and also 0.1, but the result is the same.
I did not breadboard them, i just used Proteus.
Please look in the right of the PB and you will see it there - C2.

 

The Gate threshold voltage is -1V for the PMOS. This Gate on power on is 10/110 of Vin less, which at 18V of input is at -1.6V, more than sufficient to turn on.
As Alec_t has pointed out, try increasing 100K to 220K, which should bring it to about -0.78V, so less than the threshold.

 

Thank you RamaD,
In fact is not the resistor issue, IT IS PROTEUS !!!
The Vin is 5 volts , which in this case at start should be 10/100 Vin AKA 5v = 0.5 volts
I tried what you suggested and did not works.
Then, i said maybe Proteus is wrong
Then , i disconnected the Vin, added a switch and started again with the switch open
Of course, as no Vin at simulation start, the relay or led was off.
I pressed the latching power switch, and apply power to circuit.
MIRACLE .. nothing happen and the relay was still off ( i still have the 100k)
Then, pressing the PB, everything works fine
So Proteus if i start with power off works correctly, BUT, if i start with power ON, everything goes wrong.
Please see attached