adjustable window and adjustable reset delay watchdog Timer
As you already presumed, you can use a monostable multivibrator to extend your pulse, for example using a 555 timer. If you enter "555 timer monostable" this is the first image that pops up:  

  

(Image source)

Just connect your watchdog timer output instead of R2 and the switch and connect a transistor (with base resistor) to drive the relay on the OUT pin.
Select R1 and C1 so t is 10 seconds according to the formula in the picture.