Linda will be along later to give you a lovie-specific answer but, meantime, here's some generic information. You're 100% right that the longer the chicks stay with their parents, the better birds they learn to be. Perhaps Linda will say they can have benefit of these lessons with daily playtime together and separate cages for sleeping. I'd guess though that your little family might not be tame enough for playtime outside their cage(s). Tameness is the primary reason I can think of for separating them unless you're raising them to be breeders or you intend to keep them and don't care that they aren't tame. I
think the only disadvantage of leaving them together would be danger if the parents begin to feel a little crowded. This is a very real and life-threatening problem with the cockatiels I've bred. Maybe not so with lovies
Given these considerations, once your chicks are fully weaned, I doubt there is a particular age at which separating them is advantageous. If you're able to watch closely for signs of crowding, I think the longer you can leave them together, the better for them.