Another good person to read about is RootofGood, who similarly has 3 children. http://rootofgood.com/developing-a-retirement-budget/
Both of them have yearly budgets that are safely under the low 40s (even with taxes!). I hope that helps.
We got by on around $24k/yr while working (not including child care and the mortgage). Add in a 30 year mortgage and we'd be closer to $30k while working. In retirement, we spend closer to $32k (more health/dental and discretionary expenses). Our oldest two kids are 7 and 8, and so far they haven't cost us much at all. Food is probably the main expense. Some here have suggested our costs will rise as the kids get into their teen years, and there's probably some truth to that. But it's really up to you to decide how you spend money. In general, there has been a lot of lifestyle inflation in raising kids the last few decades. A lot of that is optional.
OP, it might make sense temporarily to stay at home with the kids until they are in school. Maybe after they are in elementary school you can find an employment situation that fits around your kids' school schedule. Our kids' school also has after school care that works out to around $1500/yr/kid and would let you work a full 9-5 schedule.
For housing, it's okay for kids to share a room, so you could get by in a 2 BR house/apartment for quite a while. Our 3 kids share 1 room (by choice), leaving us with 2 unused bedrooms. That will change at some point, but for now, we have a lot of unused space in our house. For cars, we can fit 3 kids in the back of a 14 year old honda civic sedan. For longer trips, we take the larger 14 year old Accord. Having 1-2 doesn't mean you have to get a large silly car. However. we'll probably upgrade to a single car that's bigger whenever our cars require replacement (since we occasionally want to haul more than just us and our 3 kids).