You are in a stable financial position - no new house is worth risking that. I definitely would not consider moving until the EF is at $12k and you have filled sinking funds beyond that and you are saving 15% monthly to retirement.

Home Maintenance: 1-2% of home value/year

Vehicle Maintenance: $75/vehicle/month

Vehicle Replacement: Estimated monthly payment

Personal Care: Annual clothing + haircuts/12

Holidays/Birthdays/Gifts: As you see fit

How many months’ expenses does that $10k EF represent?

Do you have additional savings in the form of Sinking Funds (for home / vehicle maintenance, vehicle replacement, clothing, child activities, etc)? If so, what do those funds amount to?

Are you saving for retirement? How much is currently there & what are your monthly contributions?

If you get the EF up to 6mo expenses and you have well-funded sinking funds and retirement is on track… you could possibly consider a different house. With interest rates double what you currently have, I doubt it would be any bigger unless you go much, much further out from the city - at which point you might struggle to find a small enough lot to keep it affordable. Perhaps as you save they will creep down a bit more, but I wouldn’t anticipate seeing sub-4% rates again for many many years. Low housing expenses offer your family a ton of security & flexibility, particularly while raising several children.