There's an unequal power battle in my house, there's somethings I do more than my sister and in all fairness, there's things she'll do more than me. I also have to keep in mind that there's things my mother does more than either me OR my sister. I think what I've come to learn is that when it comes to issues like cleaning, it's a trivial arguement. Please keep in mind I'm only talking about me and my experiences, I don't necessarily thing EVERYONES household problems are trivial (just thought I'd throw in that disclaimer before I upset anyone unintentionally!!) Like I was saying, around here - it's trivial, there's really no point in me getting upset/angry/frustrated/etc about something like who put what dishes where and who didn't load/unload the dishwasher. If there's dishes to be done, I'll clean them. If the dishwasher is finished it's cycle, I'll unload it. Yes, in the beginning it was frustrating - I didn't see why I should bother considering 90% of it wasn't mine - but the thing is I was getting frustrated and angry, eventually I thought well...why? Why am I getting upset and letting something that takes a few minutes, ruin my day? Once its all done, it's done and I know my mum appreciates the help. It does my head in because my sister and I share a bathroom but since she moved home, she's never cleaned it - it's either my mum or I who have to do it. But again, I COULD spend the day being bitter and angry OR I could just get it done and be in a good mood afterward.
As I was saying, that was just my experience, my advice though is...yes it may be a battle and chances are it's a battle you won't win (just going by what you said about your parents), so I think if I were you, I want to say "life handed you lemons, so go make lemonade" or "deal the cards you were dealt" type thing. Like - yes it sucks, I agree, but maybe turn something negative into a positive?
Or suggest a chores-chart :D