I personally never enjoyed the idea of putting the female in the breeder box, as you have to time her birth perfectly. If you put her in too early, you could stress her out and she could abort the underdeveloped fry. If you put her in too late, the young fish will most likely be eaten since they were probably birthed in the main tank.
If you plant the tank densely, you can let the mother birth at her own pace, and the fry will have a better chance of survival. However, your betta seems to be the biggest threat. Being pure carnivores, they may see your baby platies as more moreso than the parents of the fry might. It's in your betta's nature. You can temporarily remove the betta, and your fry will have an even better chance of survival.
Keep in mind that platies give birth to anywhere between 2-20 fry at a time, so if your fry do survive and grow up to adulthood, have some homes picked out for them so to not overpopulate your tank. 10 gallons can only hold so many fish.
Good luck
