Hi - I was based in Secret Harbour for a reccie April/May this year. Didn’t get the time to look at the schools, so can’t help you on that one but I really liked the place and got a good vibe. The Whistling Kite has a mixed reputation, but I found it does decent meals and staff were welcoming of our kids (aged 9 and 5). We often walked back to our rental in the dark after a meal and felt as safe as houses. The shopping centre is not great but was undergoing a major expansion that I think might have opened now?
You’ll find it dead easy and quick to get to Mandurah from there (btw I liked Mandurah too!).
For getting into Perth, we used the train stations at Warnbro and Rockingham rather than Mandurah. Struggled to get a parking space at Warnbro, but Rockingham has an overflow across the main road that has loads of spaces.
As VeryStormy said above, don't commit yourself to a suburb until you get there but have a shortlist of half a dozen or so, as a few that I thought I would like just didn't feel right.
Hope your visa comes quickly!