Ah, I had a Silver Lyretail Molly that did this the first time she gave birth. I was so upset. I agree with OSagent23 with covering the tank and turning out the lights. I also learned the hard way that "Peeking" sooner than three hours was a bad idea as she would eat anyone she saw in an instant!
The babies sometimes need more than that first second to right themselves and swim off, so dense planting, not just shorter plants like grass, but larger plants that are thicker and keep mom from being able to shoot after them also help. I've found that very determined fish will dig in the shorter plants where they know there are babies until they get them. Even well-fed ones, if you have greedy fish like I do. LOL
I have also found it's better to move mom one or two weeks before she is ready, this allows her to acclimate to the new tank. Or you could move everyone else to a different tank if you have one. Less stress for mom, but then chasing around other fish with her in there would probably be about as bad...my fish are kinda dumb and were easy to remove without stressing everyone, they come right over...not everyones do that. So yeah, if you have a ten gallon tank, or even something bigger, you can use it as a nursery and/or a birthing tank. I had a ten gallon birthing tank, but since I have so many giving birth, I had to make the twenty gallon a nursery.
So in short, like others have already said...lights out, cover the tank, make it as dark and quiet in that area as you can for a few hours. Most likely after giving birth, she may sleep instead of trying to hunt in the dark, giving you a chance to quickly move her elsewhere. And many plants, big and small, tall and short, thick and thin. lol If you can't move your other fish or don't have another tank, you could divide the tank. However, you will have to make absolutely sure nobody can get by, baby or adults, as some babies can squeeze by the divider. I've found sometimes stuffing plants and rocks by all the bigger holes helps, but I've yet to find a way to make it absolute...even though I say try to. ^^;
I hope you have better luck next time. With platies, just like any livebearers, if they have one batch, they will most likely have another one within 2 to 4 weeks(Most livebearers can drop fry that often for several months without mating again). My Gold Platy dropped two rather large batches only two and a half weeks apart, and she did not have to mate again. I had no males at the time and purchased her pregnant. She's looking pregnant again, so it'll be three batches in two months, or so it seems!
Oh yes, just a tip in case you don't already have feeding plans! You may already know better. lol You should try to give your fry a variety int heir diet, all your fish really, and feed the babies three times per day at the minimum. Also, be sure to do a tad extra cleaning in their area, not a lot, just about 2% per day, suck up all uneaten foods and the like. This will help them grow faster, brighter and healthier! As for feeding, I have baby mollies, guppies, platies and swordtails...I've been breeding them just over two years...Boy do mollies grow fast in comparison to all the other livebearers! Ahem, anywho, I feed them baby brine shrimp, daphnia, minced up spinach(You have to really shred that stuff because it's hard for the youngins to pull apart when so small), romaine lettuce if they'll take it...and the frozen food Emerald Entree, one of my favorite things to give to my fish because it is full of different veggies and proteins. You have to pull the big worms and shrimp out though, they can't eat it...but it wont stop them from trying! And turn some tropical fish flakes into dust to give them at least one of those meals per day. It has calcium and other things babies need to grow well. The brine shrimp helps keep colors very bright to boot, and they love it! Give them more veggie matter than meats though. Every other day/every two days or so I give them a little shrimp or daphnia. =)
And also, keep the temp at about 79-80 degrees.
I know, I wrote a book! I hope some of the info is useful for you. I get babies in a lot and it never stops being exciting! :3