The answer to your question lies with the verb complain.
When you think that to arrest her father is a valid complement, you're treating complain as if it were the same as ask or want :
She asked the police to arrest her father.
She wanted the police to arrest her father.
But complain is not quite like those verbs. We complain to someone:
a) about something
b) that something is such and such ...
c) IN ORDER TO do something on our own behalf
d) IN ORDER TO have them do something on our behalf
It is the sense of "in order to" which makes complain different from ask and want.
This doesn't make sense:
She complained to the police in order to arrest her father.
because she wanted them to do something:
She complained to the police in order to have them arrest her father.
She complained to the police in order to have her father (be) arrested (by them).