Cut potatoes into 1/2-inch pieces. Core and chop tomatoes. In a 5- to 6-quart pan, combine potatoes, tomatoes, broth, chilies, and garlic. Bring to a boil over high heat; cover, reduce heat, and simmer until potatoes are tender when pierced, 12 to 15 minutes.
While potatoes simmer, trim off and discard excess fat from pork. Cut pork crosswise into 1/4-inch-wide strips, then cut strips in half. To a 10- to 12-inch nonstick frying pan, add oil and pork; cook over medium-high heat, stirring often, until pork is lightly browned, about 7 minutes. Remove from heat; set aside.
When potatoes are tender, stir in pork; simmer just long enough to warm meat through, about 2 minutes. Add 1 or 2 drops of hot sauce, if desired.