It's hard to know where to start, as there are so many staggeringly insane categories.
The grocery budget is insane. Create a list of 8-12 recipes that can reliably be made for less than $2 per person. That's not even all that low, really. And eat a dinner from that list those twice a week. When you are cooking them, see if you can't easily (and with almost no extra time) make 3 instead of one, and freeze the other two. Having a couple lasagnas or broccoli cheese casseroles or whatever in the freezer at any given time will help prevent you from resorting to ordering in or buying expensive prepared foods. Consider making it a family afternoon one Saturday a month, where everyone chips in (the 14yo cuts carrots and onions while the 11 yo stirs a bowl while mom browns ground beef while dad assembles a recipe). At the end of 90 minutes, you could easily have 20+ prepared dinners, ready to pop in the oven, crock pot, or a pan on the stove. Doing it all at once will help you take advantage of economies of scale, will prevent food waste, will ensure you always have a stash of foods so you aren't tempted to eat out or buy prepared, and will allow you to focus on cheap recipes that you like, all while spending time with your family. Look for cook books labeled "OAMC" or "Once a Month Cooking". Even if you don't decide to go all in with a big monthly cook, you can get recipe ideas. They tend to be fairly inexpensive and freeze well, which goes back to the "make 3, eat 1" suggestion.
$400 per month ($4800/year !!!) on gifts?! Um, just buy less stuff. Set a budget. $200 per person for birthdays (which is still a lot!) and $600 total for Christmas (assuming you celebrate it, and that's still a huge budget!!), plus maybe $600 for other birthdays or weddings that come up, and you've still cut that number my more than half. Really, your number here is just insane.
$240 for homeowners insurance seems very high. Shop around, and make sure you aren't over insured.
What is the $265 for household; maintenance? Is they really maintenance, or is it also cute new throw pillows and a new comforter for your daughter because she was sick of the old one, and a pretty new vase for the front entry, and...
$500 on clothes?!?! Again, that's insanity. Do your kids get an allowance? Are you buying them high end stuff? As you said, they outgrow it fast. Go cheap. If they don't like it, they can supplement it with an allowance (if they have one, though it isn't listed as a line item). The 14yo is old enough to babysit, mow lawns, pet sit, etc. The 11 yo could do some of those things as well. If he's out growing shoes and clothes that quickly, buy a a thrift store. At at the very least, a resale shop.
Your kids' activities are also really pricey. If she's not Olympic-bound, is there really no cheaper gymnastics studio than $330+? You say that you hope that will go away when she starts high school, but it seems to me like most of the time, kid expenses go *up* in high school, since most kids are in at least once activity there. Also, there will be prom tickets and dresses, and things like that. (It would be great if she had to pay for those on her own, but I don't know your plan.)
