Anna,
I have a couple of questions and observations. You may not be willing to share the responses, in which case, they are simply food for thought, but it would help us understand your position better if you were able to answer them.
You've obviously done well to have a paid off house in your 30s, particularly with a SAHP. You are making a lot of great decisions. I particularly like how you are giving your young kids a lot of mind-expanding experiences (zoo, museum) that are low cost and yet really memorable - some of my best childhood memories are from days like this and I'm now in my late 40s. But you are asking for critique and areas of improvement, so my comments are focussed in that direction. Your current spending amounts to over $85k a year. Depending on your income levels, this might be disastrous or perfectly manageable. Are you salaried or is your income lumpy? How secure is your job in a downturn?
Is your $545 a month your super contributions or your insurance within super?
Overall, your insurance expense looks like a lot, unless I've misunderstood. It might be worth critically assessing what insurances you and your partner need. Eg, at the moment you're paying for income protection for your partner, but he's currently a SAHP earning no income? What income is being protected there? Does your partner need $1.8m in life insurance with a fully paid off house and money already in shares and ETFs? You might only need disability cover depending on what you and your kids might choose to do if the unthinkable happens. What life insurances do you have? Are they appropriate and necessary for your life situation? Mrs G and I were at a similar point when we were your age and we decided we were better off putting that money into growing our own ETFs, in effect self-insuring, rather than paying a life insurer - obviously YMMV.
Also, your home and contents insurance may be expensive (or it may be ridiculously cheap if you are heavily exposed to natural hazards). It may be worth shopping around on this at your next renewal.
What changes to your spending do you anticipate if/when your partner's business commences? Will you have daycare/after school care expense that you don't have now? Are there start up costs that you will have to bear? Will you be able to cut aircon/heating during the day because no one is home? Will he require another vehicle which will be funded by the household? What income will this deliver as well? Do you currently get the Private Health Insurance Rebate and will this change your rebate if your partner generates an income?
I note you don't have petrol listed as an expense. Is this an oversight? Is your car full electric (note that this could explain why your electricity bills are higher than most expect)?
$70 a month on vitamins is a lot for fit and healthy adults in their 30s, with young kids (assuming you are fit and healthy). What are you not getting from your diet? If possible, can you spend that $70 on fresh food to provide what you are otherwise missing?
There's a lot of talk about air con, but I'd also look at your heating. Do you run it 24/7 during winter? If so, is that necessary? My MIL lives in one of the coldest places in the country and doesn't run heating 24/7 in winter. It goes off about midnight and not back on until someone gets up. It's on for a few hours in the morning and then off for a few hours in the afternoon, then back on before the sun goes down. I don't think I've ever felt cold there, but her place is very well insulated as well. Maybe your profile of when you might run heating/not run heating is different with the solar panels to maximise their contribution - they're obviously not as effective in winter, but they still make a contribution.
Do you have the ability to break down your additional spending? You need some 'fun' money. You MAY reduce here. You may decide you don't want to, but it's hard to assess whether you're getting 'value' from it without finer categorisation.
Finally, the elephant in the room - your In Law's mortgage. Family involves a bunch of complex decisions. I know that I would help my parents and MIL if I could and do it in a heartbeat. But it's also a drain on your own financial wellbeing. Optimising $5 and $10 here and there whilst having an expense of that size in the mix is challenging - in context, that's all your electricity bill and half your gas. It may also be completely non-negotiable. I suspect you've been through the wringer on this, but it's worth thinking about whether there are controls around this that can limit your loss on your MIL's poor money habits.
All in all, you're on the right track though. Keep up the good work!