Deciding when you're going to move the babies in with the parents depends on lots of factors. So species are more predatory than others. Platies seem, to me, to be fairly good. Once the babies are about 1 cm long, they're probably fine with the parents, particularly in a planted tank. My halfbeaks are absolutely fine with youngsters around 1.3 cm long. Other species are more predatory, and both guppies and mollies have a bad reputation for eating their fry. For them you'll want to wait until the babies are about the size of a neon tetra, say 1.5 to 2 cm long.
It also depends on other tankmates. Angelfish, pim pictus catfish, and most tetras are adept at eating fry and will not hesitate to do so. It's unwise to put in anything small with them. Since angels will gobble up neons without a second thought, they shouldn't be trusted with anything smaller than those.
Personally, I like to err on the side of caution. It's also a good idea not to mix parents and offspring unless you deliberately want to cross breed them. You run the risk of in-breeding. Far better to sell off your baby fish, and buy in "new blood" with the proceeds. Most aquairum shops are happy to take in good quality, locally bred fish because they're pre-adapted to the local water chemistry. Locally bred fish also tend to be hardier than wild-caught fish and more willing to take things like flake food, though this refers more to things like halfbeaks than standard livebearers.
Cheers,
Neale