Dear me.
For a start, going back to the adjourned meeting, we have just had a very long and tedious discussion about the ins and outs of adjourned meetings.
The discussion can be found here:
http://www.flatchat.com.au/forum/another-day-in-paradise/no-quorum-at-agm/
For your purposes, you can’t turn up at an adjourned meeting with proxies and use them. Those proxies have to be in place at the original meeting. So it is arguable that the current EC is invalid.
So, you could say to this recalcitrant trio that their election was invalid, but it may be a bit of a waste of time arguing with them, because they sound like utter pains (not to mention very rude).
From what you have said, it sounds like your scheme is not functioning (and at least one of the issues you raise could have serious health and safety/liability issues) and you may likely have grounds to have a compulsory strata manager appointed. To do that you need to make an application to the CTTT. The advantage to doing that is it will take matters out of the hands of these people entirely, but it will also take it out of your hands.
Do you have a strata manager?