She began to wish she could sit on it.
and banged the door shut. - 'banged' is possible. It is the sound the door makes when it is slammed shut...so, 'and slammed the door shut' is another way of putting it.
When suddenly she heard some shouts from outside. - 'when' would be correct if you had written : She cheerfully waited for the chick to sleep, when suddenly she heard some shouts from outside.
Otherwise : She cheerfully waited for the chick to sleep. Then suddenly she heard some shouts from outside.
She got scared and shrank behind the cupboard. She hit her shin on the cupboard : try to avoid using the word' got' in the children's writing, and yours. Instead, 'she felt scared', 'she became scared'.
and she fled (way-omit) leaving her wish unfulfilled." You changed the tense by using 'had', and it doesn't follow logically from just capturing the dog's attention. If you had written: '...dog's attention and he started to chase her. She had to flee...'
'away' is implied in 'flee' We would use it if you had written, ...and she had to run away, leaving...