Hi Jan,
Many traditional carnitas recipes call for the pork to be simmered in lard until tender and that may explain why it's so delicious at your great Mexican restaurant. No matter how delicious, I just can't bring myself to cook carnitas this way.
Here is a recipe you may want to try:
Carnitas Recipe
4 pounds boned pork shoulder, trimmed of fat and cut into large chunks
3 - 4 cups beef broth
2 cups chunky tomato salsa, homemade or store bought
Water
Salt to taste
In a large, heavy saucepan or Dutch oven over medium-high heat, combine pork, broth, and salsa. Add water until the meat is completely covered. Cover and bring to a boil. Reduce heat to low and simmer, until meat is fork tender and pulls apart easily, 3 - 4 hours.
Add salt to taste if needed.
Preheat oven to 400 degrees. Remove meat from liquid in pot and discard the liquid. Place the meat in a roasting pan and break it into small chunks. Roast meat until browned and crispy, about 15 to 20 minutes.