This sentence is technically ambiguous, but it is typically interpreted as an indirect passive sentence with some implicit subject. Let's assume the implicit subject is 父親, and compare your sentence with a typical indirect-passive sentence:
I had my wallet stolen.
[My father] suffered on account of me being taken. / [My father] was deprived of me.
A sentence like 1 should be found in any textbook. And this is why を is used instead of が here. The subject of this sentence is not 私 but someone else mentioned in the previous context!
Note that に in 人質に is almost certainly a role marker rather than an agent marker in your sentence. This part requires common sense rather than grammar; it is unusual for a hostage to kidnap someone.
I had my wallet stolen by a thief.
[My father] suffered on account of me being taken as a hostage.