Seed and dice the Roma tomatoes. Dice the avocados, red onion, and bell pepper. Seed and finely dice the jalapeño, then chop the cilantro.
Rinse and thoroughly drain the black beans and black-eyed peas. Place them in a large 4-quart bowl with the completely thawed corn, tomatoes, avocado, onion, bell pepper, jalapeño, and cilantro.
Whisk the olive oil, lime juice, red wine vinegar, sugar, salt, black pepper, and garlic powder in a small bowl until evenly blended.
Pour the dressing over the dip. Toss thoroughly but gently, keeping the beans intact and the avocado in visible pieces.
Serve immediately or refrigerate until needed. Stir gently before serving because the dressing will settle. Serve chilled or slightly cool with tortilla chips.