If what you say is true (and I have no reason to believe it isn’t) your new strata manager has pretty much proved that she is the last person you would want to run your scheme.
Anyone can be elected to the EC provided they are nominated by an owner who is not standing for election. A co-owner can’t nominate him or herself but they can be nominated by their co-owner (I’m guessing this is the situation with your secretary).
The appointment of the new strata manager by the current secretary’s OK was not legal. This required the approval of a general meeting.
The easiest way to resolve this is to hold a quick EC meeting to remove the secretary and replace them with someone on the EC whom you can trust (you?).
Once you have a new secretary in place, cancel the meeting and issue a new agenda with the items you require on it. The fact that your “new” strata manager has even considered putting anything requiring a decision under ‘general business’ at a general meeting shows that she is fundamentally incompetent. Add to the fact that she has manipulated the proxies so that they all approve her appointment and I wouldn’t even consider her for renewal, except for this: You want all the documents related to the strata scheme to be brought to the meeting so you have to let her think she’s in with a chance of keeping the business.
Contact a couple of other strata managers (and I would include our sponsors Strata Choice among them, if only because they would be sponsoring this website if I didn’t rate them) and you could even ask if they’d be prepared to help with this process without any guarantee that they will be signed up.
Your strata manager’s behaviour is extraordinary and either shows a lack of knowledge of strata law or a preparedness to ignore it. Either of these would disqualify her from re-appointment, in my book.
Act quickly and decisively and all this will soon be behind you.