Fill a large pot with lightly salted water; bring to a boil. Cook meatballs, working in batches of necessary, in the boiling water until they begin floating on top and are heated through, about 3 minutes. Remove meatballs with a slotted spoon, drain in a strainer, and transfer to a large saucepan.
Combine ketchup, apple jelly, red currant jelly, and hot sauce in a separate large saucepan; cook and stir over low heat until jelly is dissolved and sauce is heated through, 5 to 10 minutes. Pour sauce over meatballs. Simmer, stirring occasionally, over medium heat until meatballs and sauce are thoroughly heated, 15 to 20 minutes.
The amount of sauce in the recipe works for up to 5 pounds of meatballs, if you make more, you will need to increase the sauce. If you cook less meatballs, you would just have more sauce. The size of your meatballs may change the number of servings. My approximately 32 serving count is based on 5 pounds of 5/8 oz sized meatballs (about the size of a golf ball) and about 4 per person.
You can also simmer the meatballs in a slow cooker. Transfer cooked meatballs from boiling water a slow cooker. Pour the simmered sauce over meatballs. Cook on Low for about 1 hour.