3 years sounds like it's pushing it a bit, you'd only have 52k a yr on 1.3 mil on a 4% SWR, it's certainly possible and people get by on half that. I live in a HCOL Area(NYC) also and i get by on 40k a yr for a family of 4, though our housing cost is a bit lower as we do own our home, but our budget is much more barebones than yours. It might not be so easy to cut your spending in half even if you move to a cheaper area. Living a frugal life style isn't easy, it takes time to adjust to the lifestyle and self control on spending. Also things to consider, kids cost more as they get older, cell phones, video games, laptops, cars and college tuition. It's also up to you if you think its worth it to move to a more suburban area that lacks the conveniences you now have, the kids certainly might not be thrilled about it and leaving their friends behind.
Current expenses:
Rent (don't own a home) 3500 - maybe you could shave off 2k on this once you move to a LCOL area
Grocery & household 500 - maybe can cut down by 100-150 on this category a lot of threads here on food budgeting
Eat Out 300 - can cut this in half or less if you stick to once a week cheap lunch outings.
Entertainment 200 - Can cut down on this by looking for free activities.
Misc. (One time buys / Clothes / Shoes etc) 200 - Can cut down on some of this, though I know your kids will get older and this expense might even increase
Car (gas, ins, registration & maint.) 230
Cell 160 - There's certainly cheaper plans out there, $160 is a bit pricey for 2-3 lines. There's certainly cheaper options out there. I would think at your salary the company might even qualify this as an expense along with cable if you do work some at home after hours.
Utilities (pge(75), water(60), sewer(40), trash(30), heat(10), bankfee(30), internet(65), home phone(45)) 375. Bank fee what's that for? it's usually not good to pay any bank fees. Home phone is obsolete $45 when you all have cell phones.
kids classes 100
kids tuition 300 - If you move you might be able to find good public schools and cut this expense, but at the same time it cost more to live in a good school district so that may cancel out any savings.
kids school 50
Life Insurance (health issues for me) 400 - i guess you can cut this down once you've built up enough for FIRE as you can self insure.
Healthcare (Prem. + OOP) 600 - This will only get a lot more expensive if you have to pay the premium on your own until medicare kicks in at 65. This could cost up anywhere from 10-30k a yr depending if you get ACA subsidies.
Vacation 550 - You could take cheaper trips, but I suspect this could even double if you're FIRE'd as you'll have a lot more time on your hands.
I think you should try cutting down to close to your fire expense level now while factoring the savings you might get from renting in a LCOL area. But unfortunately a lot of those savings might be null after you add in the extra cost of expensive health insurance premiums, so your expenses may still remain around 90k. The good new is you have a lot of fat you can trim now and it's a good idea to see if you can live on a lot less between now and your FIRE date. You should definitely have a more detailed spread sheets and plan out some scenarios on how much rent would cost for the area you wish to move and how much health insurance might be at your expected FIRE income level.
I think pushing the fire date out and saving closer to 2mil might be a more comfortable lifestyle for yourself, but you can certainly reduce this number if you can get your expenses down. Just don't wait until it's FIRE time to cut back, start sooner and see if you're even comfortable living more frugally.
As far as leaving money for the kids. Most likely you won't deplete your investments by the time you're gone if you're only taking out the 4% SWR. I have 2 kids and I wouldn't work an extra 5 years to give them privileged lives. I grew up with nothing and built everything I have with hard work and I'm proud of it. I think the best thing you can do for them is to pay for their college so they won't have debt when they graduate then they can work hard and build their own wealth without student debt hanging over them like most people have. Of course if your finances are still good by the time they're ready to buy a house maybe you can help them out with a down payment. Otherwise they would get what's left when you pass, which can help them fund an early retirement. I certainly don't think anyone should inherit 1.5 million at a young age, I think it will make them lazy and not ambitious if they knew they were set for life.