The use of 'my' is rather unavoidable. But I understand the desire to remove any affectionate connotations from it. This can be done with some additions.
'I grew up watching my monstrous father...'
'I grew up watching the demon who called himself my father...'
You could also make 'mother' the subject, rather than the direct object, if you switch the verb to the passive voice. Then you shift 'father' away from the focus of the sentence and into a prepositional phrase.
'I grew up watching my mother being barbarically assaulted by my beast of a father, as he wreaked havoc around the house night after night.'