If the vote was conducted using an “assumed” proxy but without any signed proxy form, you can certainly challenge this at Fair Trading and the CTTT. In simple terms, you only need 25 percent of effective votes at the meeting to knock the by-law over. It might be worth checking if the other votes were valid too – if your rells hadn't paid their levies, they can't vote. Also, look at unit entitlements – they can come into play in a tight vote and you could, theoretically, have 25 percent of them even with your absent uncle's vote counted.
To be honest, your building sounds so dysfunctional (I recall your previous posts) that I would be applying to the CTTT for the statutory appointment of a strata manager to get all your common property repairs issues dealt with properly.
In fact, before you do anything, talk to a specialist strata lawyer. It will cost you money but it sounds as if you are so far behind the eight-ball on this and other issues that a moderate investment in legal advice will reap serious benefits in terms of the value of your home.
But first, call Fair Trading on 13 32 20 and ask for a mediation which is the first step you must take before action at the CTTT.
Manwhile, have a look at the rest of our 'Pets or pests' forum where you may find some encouragement. And don't worry about the dog – there's a lot of hoops to be jumped through before your pet is evicted – if, indeed, that ever happens.