The baby didn’t sleep well.

You could also say, "The baby wasn't sleeping well."

It was usual due waning.

Не знаю, что это значит.

The boy yanked the cradle, was trying to calm him.

To "yank" means to pull hard (дергать). Instead, you can say, "The boy gently rocked the cradle, trying to calm him."

If the baby keeps crying, his mother will have to break off her date and return home.

If the boy can't keep a solemn promise to look after his brother, his mother will say he is a hopeless dumbass.

The word "dumbass" is informal slang.

He is already accustomed to it.

Hi will embarrassed fiddle the thawing chocolate and squeak like a gnat was requesting for leniency.

Извините, но это просто бред.