How exciting to get 4 babies from a first clutch!

It is not unusual for eggs and/or babies to find themselves out of the nest. Usually, it is by accident - if either parent is frightened out of the nest and the baby or the egg was under the parent's leg. I'm not sure if you actually observed the male throwing the baby or the egg out or not, but otherwise, I would be inclined to think it was an accident. Other times that a baby is thrown out, it is often (but not always) because there is something wrong with the baby and it may not survive anyway.
The female can raise the babies on her own, as long as you have an abundant supply of food and water available for her. Now that you have removed the male, I would probably leave him out until the babies leave the nest on their own. At that time, you could put them in with the male to look after and give the mom a break - or you could put him back with the family. Keep an eye on him though to make sure he doesn't hurt any of his babies. You could also leave him out and let mom raise them completely on her own.
Please let us know how things go with your little family.
