Preheat oil in a large saucepan or Dutch oven over medium-high heat.
Mix the flour with salt and pepper. Dredge the chicken pieces in flour, shake off excess and fry until golden brown and meat is cooked through. Remove from pan and drain on paper towels.
Meanwhile mix water or chicken broth with mole sauce in large skillet and heat, stirring to dissolve mole. When mixture comes to a soft boil add the chicken and simmer. Adjust seasoning, as needed with additional salt.
For the Salsa Relish:
Mix all the ingredients together in a large bowl and set aside. The relish can be made up to 2 hours ahead, do not refrigerate.
Preheat oven to 375 degrees F.
On a large heat proof platter, spread 1/2 the bag of tortilla chips then layer with 1 to 1 1/2 cups of the shredded pepper jack cheese covering all chips.
Spoon about 3/4 cup Salsa Relish over cheese (or as much as you like, but don't use all of it, save some for serving on the side). Spread refried beans on top and layer with remaining chips.
Sprinkle 1 to 1 1/2 cups of shredded pepper jack cheese on top of chips. Spoon the Chicken Mole on top of cheese and place into the oven. Heat in oven until cheese melts.
Remove from oven and top with remaining cheese, quartered olives and diced avocado. Dollop Crema Mexicana on top of this, as much as you like.
Garnish platter with lime wedges and serve with remaining salsa relish on the side.