Hi there and welcome to the forums!
Is this chick fully feathered and well developed?
If possible, can you post a photo of the chick for us to see?
At 1 month old, the chick should be well on its way to wean and should have already started to come out of the nest to explore the world outside.
If the father is being violent towards the mother, then it's best for you to separate him from his family and place him on a different cage.
You will have to pay close attention to the mother to see if she is taking good care of the chick. If need be and given the delay on this chick's mental (and possibly physical) development, you may need to supplement feed it: https://talkbudgies.com/budgie-breedi...ing-guide.html
If you haven't done so already, you should encourage the chick to eat on its own by placing half a spray of millet inside the cage.
You can also place some veggies by nest box's entrance for the chick to eat.
When you take the chick out of the nest for taming/socialization time, you can also set up a little feeding station with some seeds/pellets, egg food and veggies. https://talkbudgies.com/articles-budg...me-chicks.html
I hope your chick will soon catch up and is able to wean well and gain its independence.