How old are your kids? Are they in school or will they attend school?
As for your Save to Spend category, I see this as something different from an emergency fund.
I used YNAB for budgeting and find it helpful to conceptualize spending in various ways. I'm not saying you make categories of each of these but it helps me:
1. Monthly bills - both fixed and variable. Take mortgage or electric bill for example. You can usually forecast these with a fair amount of precision.
2. Irregular expenses that are fixed or are not all that variable. For me, we pay garbage quarterly and it is a fixed amount. Property Taxes, annual insurance, etc. Automobile maintenance (not repairs) also fit in here.
3. Expenses that are irregular and very variable in amount and you expect you will have them at some point but don't know how often. This is what you have mostly in your save to spend category. For example, I might in one year have a couple of thousand dollars in auto repairs and have none the next year. The point is that these are highly variable. Some people look back at past spending and come up with an average annual amount and then set aside 1/12 of that each month.
What I do instead of doing this by each expense is I have set aside an irregular expense fund. I basically set that aside to cover all the irregular expenses that might occur during the year or might not. If I don't have all of them this year then I usually role it over (you can set a maximum for it).
4. Major things you want to save up for. Car replacement, new roof, etc. The one that I wondered about on your budget was down payment since you say you already have a house.
So I would still keep set asides for irregular expenses but you might combine some of them into a single fund. This is different from your emergency fund.
Now - having said all of that - I wonder about your budget. You have very little spending in some categories particularly for people with children. You used I always did pie in the sky budget that were based upon nothing ever going wrong and they were more aspirational than realistic.
I notice you have no child related expenses. No clothes, no toys, no books, nothing. As a parent of 3, I have found that kids particularly as they get older do cost something to raise. Even without being extravagant most parents will want their children to have some toys, some books and will find that their children grow and need clothes or shoes or underwear or socks.
Once children are in school (whether in a physical school or homeschool) there are school supplies, school projects, and other expenses. Some kids play sports or take lessons. Again, not saying you need to be extravagant but your budget looks like you don't even have any children.
Also, what about clothes for you and your wife? Again, not saying a lot of clothes are necessary but most people will need to sometimes buy shoes, underwear, a coat, and other clothing.
Personal care? What about haircuts? Makeup?
I assume you have a computer or two since you have internet. What about software and budgeting for a computer replacement? Paper for your printer? Ink? Postage for mailing stuff?