Upvote:3
What you are proposing is known as a "visa run". Australia does not have a set limit for how many times or how long in total you can stay in the country on tourist visas like eVisitor, and it does not ban back-to-back entries on a tourist visa, so visa runs are possible -- some stories here.
However, tourist visas are meant for tourism, which is clearly not what your partner & children would be doing in Australia. Whether they'd accept "hanging around, supported by Aussie husband, while we wait for visa" as an acceptable reason is unclear. Immigration has the final say in whether they get in or not, and may suspect that your partner is working.
The safer and cheaper approach would be to approach Immigration towards the end of your three-month stay and ask for an extension of a month or two, which are (anecdotally) fairly freely granted.