I'm very sorry for your predicament.
Do you currently have another pair breeding at the moment that could possibly foster the youngest chicks, including the hatchling?
This would be the best option to ensure the safety of your chicks as well as the chances of their survival.
There could be a combination of factors that has made your female budgie to react the way she did, as for her not feeding the hatchlings, she may have run out of crop milk.
Clearly she is not at the right frame of mind to raise these chicks and they are at serious risks of being abused and neglected.
Given the circumstances, it's imperative that you get all of the supplies (including a brooder) to raise your chicks or else tragedy can struck again.
I really doubt it was the male's fault, most likely he was trying to protect the chicks and he ended up getting injured. How is he doing now?
Due to this tragic outcome, it's best that in the future you no longer allow this hen to breed and this is even despite her wish to do so.
From your description, it's very likely that your budgie is a chronic egg layer, since she was so determined to nest and lay eggs even without being encouraged to do so.