Combine the olive oil, white wine vinegar, lemon juice, minced garlic, chopped parsley, salt, and pepper in a small bowl and set aside. Place the whole red potatoes in a medium-sized saucepan, cover with cold water, and season generously with salt. Cover with a lid and bring to a gentle boil over medium heat, then uncover and cook for about 15–20 minutes or until the potatoes are fork-tender. While the potatoes are cooking, trim the ends off the green beans. Bring a separate pot of salted water to a boil, add the green beans, and cook for 3–5 minutes until they reach a tender consistency. Once the potatoes are cooked through, drain thoroughly and cut them into large chunks. Combine the warm potatoes and green beans in a large bowl, pour over the prepared dressing, and toss gently to coat. Transfer to a serving platter and present warm or at room temperature.