Hi Joyeux,
My cousin recently moved over to JB also.. She tried applying for RHB bank account.. They required her to provide payslip and a malaysian address, no need anything else.. So maybe u can try after u move in (if u ever decide to)..
Austin/Tebrau area to CIQ is quite straightforward..

If u're working office hours, jam is sure to have one (unfortunately).. But it's 100% worth it! My cousin tasted life in JB for almost 2months now and she's really happy.. Tired but happy.. xD
Actually, both my hb and cousin drive JB cars so they take bus across causeway to SG/work.. Save a lot of money and in cases of jam, maybe can save time also.. Because of the bus lane..
As for school, if u are going to register your kid/s to school in JB, they can get student pass from the school.. We will be registering my girl next year, in an english based christian private school.. We scrapped the idea of chinese school cos they study all subjects in chinese which we are not really fond of.. That includes science and math!
For supermarketing, we buy freshfoods (esp seafood like prawns, fish etc) from Tebrau Jusco.. It's surprisingly fresh.. For everything else, we can buy from anywhere.. Tesco (few outlets), Jusco (few outlets), Giant (few outlets), even the one and only Cold Storage (mostly to buy imported goods, esp for my baking stuff) etc.. We buy depending on where we go..
When we came for viewing to rent, we placed cash deposit.. Our landlord is a chinese, very nice family guy.. And my agent is also very professional and patient.. He was also the one who helped my cousin rent her studio condo apartment.. If u want, I can pm u his contact..
Btw, the reason for us renting my current place is because it's walking distance to Jusco.. Reason being, I have no driving license yet.. Haha.. So when hb goes for work/reservist etc, we don't worry about supplies in case of emergency.. It's very convenient..
Safety wise, even in SG now I wouldn't let my eyes off my kids for a moment (unless it's fenced area like indoor playground).. Because it's not as crowded here, sometimes we will sit down on benches and let kids wander around, within our sight.. Still feel quite safe la.. No matter what still must be careful here though.. As long as we don't flaunt our "wealth", it should be fine.. I stay here for 2yrs, seems alright to me.. I can only say for my area.. Other areas, I'm not certain of the safety..
Mind if I ask how many kids u have? Are u and your hb both working? Both also SG?
Sorry for the long post.. =X Glad to be of help though!