OK - first post here, but this is because I know someone confronted directly with the exact same vexatious abuse of the Victorian IVO system.
I'm not a lawyer, but I am all over the language and some sloppy language skills which are causing all sorts of issues.
There's a few fatal misunderstanding and misinterpretations that are leading to a quagmire.
The misinterpretation(s) of this line specifically are leading to all sorts of problems:
publish on the internet, by email or other electronic communication any material about the protected person(s)".
Some have misread this to mean:
1\ email is inherently published - demonstrably untrue. An email between private recipients is no more published that a letter sent by the tradition means of normal post is published.
2\ many have incorrectly conflated ON with BY - the word by is used interchangeably with the word via depending on the date when the original IVO application was sought.
Go to a common law concept of publication and specifically "public display" - I can say with absolute certainty that NONE of the forum members or any of the general public is privy to the content of any single private email or normal letter that I have ever sent, UNLESS they were/are the intended private recipients of that correspondence, or received it from one of those intended recipients.
IF a recipient publishes that correspondence ON the internet, you may have a case of acting via a third party - that would have to be proved.
Conflating "on the internet" with "by or via the internet", which in this case is the transmission medium is as misguided as claiming that I am publishing, about someone which I may be prohibited from doing, by writing their names on a piece of paper, putting it in a envelope and posting it to "God c/o Heaven" or anyone else that I might care to send it to, as long as it doesn't end up being published in a form which is available for PUBLIC DISPLAY.
Now compare, I write a letter/email and post or email it to the editor of a newspaper about the protected person - that's an intent to publish, however it is not published until such time as it is printed in the newspaper. If it ends up in the editors waste basket, never printed in the newspaper or read out on the radio or on TV, it's never published and no-one with any common sense whatsoever would attempt to make such a claim.
Sending an email, SMS or visiting a web page to effect that same outcome of publish for public display, whichever form that may take, isn't publication until such time as the content of the communication is on public display.
How the Victorian coppers, yes among some of them it's a very low intelligence bar indeed, cannot distinguish that private email correspondence sent BY or VIA (I have seen both words used in IVO's) the internet isn't published, they like to engage in reductio ad absurdum to take that any single mention of the protected person in private correspondence with other persons as being the equivalent of publication.
How that made it past the coppers in the first place is perhaps not so surprising, HOWEVER, how that gets past a prosecutor and perhaps a magistrate as a technical breach is both appalling and astonishing.
I've seen video of a police interview where they made that specific accusation eight consecutive times about publication - this is Year 10 English comprehension about the definition of publish and the inability to distinguish between something sent BY the internet as a transmission medium as distinct from something available to the general public ON the internet - facepalm!!
The IVO's don't state "can never mention the protected persons name in any private correspondence whatsoever", but somehow that fallacious interpretation has become the norm, both with the police and some here.
Which brings me neatly to; can I publish via email on the internet - well it's a resounding YES!
There are tens of thousands of email lists related to virtually any conceivable topic or subject matter, they have been around since almost the invention of the internet, when transmission speeds were slow and email neatly accommodated the slow data rates.
They pre-date forums like this, they pre-date websites and they definitely pre-date social media. They come from an era where it was almost all text, graphics were expensive and out of reach for many and M$ Windows wasn't even in it's infancy, some would argue that it still is, but I digress...
For the email lists, also used to be known as newsgroups; After joining, if necessary, one can send an email to a list, which will have any number of recipients AND that email is on PUBLIC DISPLAY ON THE INTERNET to anyone in the world, available by going to the specific web page.
Further, it needs to be noted here that the definition ALSO INCLUDES by other electronic communication.
There are a multitude of forum reading applications, indeed Twitter had until a few years ago a 160 character limit, BECAUSE it used, at the time, SMS and MMS as a means to publish on Twitter.
Note, I specified publish on Twitter BY/VIA other electronic means.
I can publish on virtually any website which has comments, discussion, remarks or any other form of feedback by visiting the relevant website/page and typing away, just as I am here.
Twitter is just one example, there are a multitude of other ways and means to publish all over the internet via SMS or Apps on phones & tablets also, which qualifies as other electronic communication.
To the OP's other issue, communicating with the protected person's lawyer directly isn't a breach, UNLESS the IVO specifies that the respondents lawyer must communicate with the protected person's lawyer - this is an optional condition, I've both seen it specified and I've seen it omitted. In the case where it was omitted the IVO did specify that the respondent could communicate with the applicants through A LAWYER. Further into the court orders on the second page it stipulated that the respondent was to supply the response to the better details and particulars to the applicants lawyer by a certain date - they tried to argue initially that any correspondence by the respondent to the applicants lawyer was a breach - I corrected them appropriately on that point, because the first page of the interim order only stipulated a lawyer/solicitor, whereas the second page specified the applicants lawyer - the identity of "a lawyer" was now a known identity.
Note the general article "A" , not the specific article "the respondents lawyer" - it's not a breach technical or otherwise to communicate directly with the applicant's lawyer, which is almost always necessary in family law cases, unless it is specifically stated that the applicant and respondent must only communicate through their respective lawyers - this provision may or may not be included.
As far as gaining access to the OP's emails by impersonating him and unlawfully accessing his emails - that's a flat out crime and needs to be prosecuted.
The communication about her is not communication to her, nor is it published on the internet - that was a serious mistake on her part if true.
The possibility of the OP's ex partner being identified by the fact that she's in the Victorian Police - nonsense - I see nothing is his posts giving evidence as to his identity and by extension any possibility whatsoever of identifying his ex partner by virtuee of being in the Police Force. That's a group of people in the tens of thousands.
Lastly, putting photos onto any online storage medium which is password protected, isn't published, specifically because any member of the general public that does not possess the appropriate login credentials cannot see it, it is by both definition and effect private, given that she thinks that circumventing privacy to make allegations of breaches just requires some sensible application of definitions private and public, by definition are antonyms, if she's prepared to breach privacy restriction(s) to make allegations of breaches she need help.
I've got content online, private content, password protected, it's not published! - Now if someone breaches that privacy, breaks the law by either breaching security, impersonation by using their login credentials, or otherwise circumventing that security designed to protect privacy, they deserve to be prosecuted, because they've committed a crime.
Posting photos of the children to a private facebook group if they are not on the list of applicants to the IVO isn't a breach, BUT mentioning the Ex in any negative way shape or form in the process, going to potentially go for that as a technical breach I'm afraid, but if it's not derogatory or committing family violence in the process I believe a Magistrate should throw it out if it even gets that far, because it a vexatious allegation to be making in the first place.
There's some really poor language skills that have given rise to demonstrably false interpretations, these seem to have been accepted at face value and a ridiculous circumstance has been allowed to perpetuate as a result.