I have a problem with words...and the excessive use thereof. So, sorry for the overly long post.
We're living in Ballarat, just west of Melbourne. Family of four, one kid in Primary School and another in Kinder. Wife works part-time, I'm a stay at home dad. I'm sure our numbers and commentary won't be an exact fit for your situation, but maybe it'll help some nonetheless.
Basic
Food (30/day for 6 days a week, and 50 for the 7th day) 12000
We were spending $150/wk on food, with way too much waste. We brought that down to $100/wk easy, then $90, $80, and experimented a couple weeks at $70. $80/wk seems to be the current sweet spot. The main necessities (milk, bread, butter, flour, sugar, etc.) are bought at Aldi. We (mostly my wife) keep an eye on the flyers each week. When something like Kraft peanut butter goes on sale for about the price of generic (or sometimes even less), we stock up like crazy (I've bought $80 of peanut butter in one go, virtually wiping out our grocery budget for the week). Most of my wife's shopping is at Coles and Safeway (Woolworth's), frequent visits to NQR, and occasionally IGA (can't forget The Reject Shop, I think they often get leftovers from USAFoods, found the impossible-to-find Marshmallow fluff there last year!). Anyways, at $80/wk, that's about $4,160/yr.
Public school fees 2000
Have you checked any of the local schools and asked what the "voluntary" fees are? I can't remember off the top of my head, but our local primary school charged $200-something. If you got the EMA (Education Maintenance Allowance) worth around $160, and signed it over to the school, they counted that as paid in full. I think the only requirement to get EMA is to have a Health Care Card (for the non-Aussies...it's not related to Health Insurance, it's a concession card for low-income people/families; I may disagree, but we're considered low income, so there ya go). I love how it's one price, and that's IT. No needing to supply ANY school supplies (pencils, notebooks, class books, fees for excursions...ok they do ask you to provide an art smock and would appreciate boxes of tissues, but that's all). So, cost between $0 and $200-something.
School misc 1500
Wait...$2,000 in fees plus more? How? I'm guessing maybe camps, sports fees, stuff like that? I think most of that is for later grades (the grades 5-6 seem to do several camps throughout the year; I haven't kept track of the costs, but I don't remember seeing a price over $200). Am a bit curious about this. Perhaps our school just doesn't charge for a lot of things that other schools do? Or maybe you're including things like eating lunch at school (which I would include in the grocery budget)?
Kids misc 2000
What's going under this kids misc section? If you've already accounted for the kids' cost in the school, grocery, entertainment, gifts, etc. categories...what's left? Clothing and dental costs? Kids don't need $1,000 each in clothing and dental work (ok, maybe in EXTREME cases they actually NEED braces...but in general no). During school they'll (probably) be wearing school uniforms, which I assume you included in the school categories (if not...good gosh why are those so high?). Keep an eye out for good quality pants/shorts in the required school color (ours is navy blue) throughout the year at the op-shops. For the shirts, I've seen them brand-new for $2 in January. For outside of school, I'd buy everything I could at op-shops (except for underwear).
Oh, our expenses...dunno for sure. We give them an allowance of approximately $1 per year of age (I currently give a raise every third year, so at ages 4-5-6 they get $5/wk, 7-8-9 they'd get $8/wk, etc.). Divided up 40% spend, 30% save, 20% invest, 10% donate. They get to spend on virtually anything they want (I don't get the appeal on $7 trashies...but neither do they get the appeal of a gym membership...different priorities). Spend maybe $10-$20 on each for birthdays and Christmas presents. Giving the oldest a $5/mo clothing allowance once he turns 7. All up (clothing, allowances, presents) my rough calculations show under $1,000 for both kids combined. Of course this number will likely go up as they get older...by the time it would go up exponentially, they'll probably have part-time jobs, so it won't actually be that bad.
Internet/phone 1150
Ours is about $63/mo, though it can be a couple dollars over on occasion (if I had to make some calls that month). Through Dodo, unmetered (I've checked how much we use...good gosh it's a good thing we have unmetered, I blame judicial use of Netflix). Under $800/yr.
Wait, are we including mobile phones? We spend maybe $12/mo total ($5/mo for each of us for data, then whatever few calls are made on top of that), so add $144/yr to that. Unless the costs of the phones go here instead of under shopping in which case...my head hurts.
Electricity and gas 2100
I think you may have us beat on this. I'm trying to do better (last year I ran the heat during really cold nights...now we just suffer through the cold nights with our electric blankets and I turn the heat full-blast in the mornings). Low rent and no insulation = high heating/cooling bills (we still make out better financially than if we had a better insulated, and more expensive, place). Very rough estimate = $2,000/yr (as I said, very rough estimate, it could end up being $2,500 and I wouldn't be surprised).
Entertainment 500
We budget $50/mo, but tend to not spend it. I mainly count screen-time (tv, movie theatre) in this category. We may occasionally spend $60 for the whole family to watch a movie at the theatre...but as long as we're under budget, it helps keep me from hyperventilating at the FREAKIN' $10 FOR A SODA AND STALE POPCORN??!!
Shopping/gifts 2600
Is this just shopping for fun? I try not to do that. Gifts, we don't really do. If my son is invited to a birthday party and wishes to buy a gift...that's what his allowance money is for (and he did choose to purchase a small gift).
Health insurance 2600
We're pretty sure we're sticking with Medicare-only. Just in case though, we did purchase private insurance for 2-3 months then suspended it (we're a special case; had one year after arriving to purchase, can suspend if we're going overseas and back which technically we are; just bought us some time is all). I've found the medical coverage here pretty good, probably better than in the US. Strong disclaimer...no major long-term ailments, can't comment on that.
Luxury
Food 5000
I'm guessing this is your restaurant category? Ours used to be $50/wk, now it's $20/wk. Just enough for a weekly visit to McDonald's or Hungry Jack's.
Flights 5200
Holiday expenses (other than flights) 5200
I am somewhat curious why these two are separated? I look at the total cost of a vacation/holiday; maybe the actual holiday is dirt-cheap but the flights are a bit higher than normal, that's fine. I'm just guessing, but I think you're breaking it down as local holidays $5,200 and trips to Canada $5,200. I can't judge at all here, travel is extremely important to us, and "back home" is in North America. Depending on exactly what you count as a holiday/flight expense, we may be spending a similar amount.
Car 5500
Car...a luxury...good job categorizing that! Again, we spend a bit less...but with the high rego costs here, that doesn't sound too bad (I'm assuming that includes vehicle purchase price and maintenance).
Misc (add 10%)**** 5400
I love having a buffer. Because real life always seems to happen when you least expect it.
Quick FYI on our budget, we have some categories you don't, which is probably due to our different ways of viewing spending. Wife and I each get $50/mo misc money to spend however we like. Me, new android tablet. Her, gym membership. We also get $50/wk for dates, so if both kids are at school and she's off work, we can head to a nice restaurant (or to McDonald's) and have a nice meal together (note, we don't come anywhere near spending $50/wk on dates, which is actually a problem; married couples do need time just to themselves, even if it means hiring a babysitter so they can go out to watch a movie every once in a while).
Also just noticed I didn't include sundries (toiletries etc)
Those are included in our grocery budget. Virtually anything bought at the grocery stores count as groceries (toilet paper, toothpaste, laundry detergent, etc.). Notable exceptions would be things like electronics, tools, clothes (I'm looking at you, Aldi), make-up, stuff like that.
6) Part of why I split it up into basic and luxury is because I'd like to have a conservative SWR for 'basic', and a less conservative but comfortable SWR for the total. I have in mind a 2.5% SWR for the basic budget, and 4% SWR for the basic + luxury budget. The 4% SWR for basic + luxury budget should have my wife and I ER by mid 30's.
That's certainly a different way of looking at it. Me, I just have different investment goals (reach X and you can afford the bare necessities, reach Y and you can live a little, reach Z and you're living the good life).
If only I figured this out when you did. Mid-30s, still a ways off from retirement, but it's all good.