The first question you should ask is, is it worth fighting? Does the existence of an AVO impact your ability to spend time with kids/family, or do the conditions/restrictions have an impact on your work or daily life? If there's no impact, then you may be better off saving yourself the grief and $$ and just move on.
Yes, it's a kick in the guts to feel like you've been labelled an abuser, especially when many lay people don't understand that these are now issued without any evidence being tested, and assume you must have committed family violence.
Thing is, being a civil matter the standard of proof required is low- "on the balance of probabilities" and I'd argue that magistrates even err on the side of caution around that already low bar. If the applicant drops the magic word 'fear'- that's pretty well game over- how can you prove or disprove what another person feels?
How blatantly false are the statements you mentioned- alleging you were at their doorstop threatening them when you were actually 2000km away? They say they're scared and want you gone but they were contacting you in the days before the application?