Let me get this straight. If the sentence were "I love my father...mother" I would not use "của"?
You still could. There seems to be a loose unofficial rule that if possession involves one word (tôi) the của can be skipped. I think some common sense is in play for native speakers too, most of the time we reference ourselves for father, mother, wife, husband so we don't have to wave the của for clarity.
Why is DL NOT correcting mistakes since the recent update?? I put "Tôi yêu và của tôi." and it was marked right. ??? Hmmmmm.