The average cost of Daycare is $11,666. The salary a full time minimum wage worker makes is $15,080 a year. Even if someone works minimum wage they still have enough money to cover daycare,. And even if it was the same cost, then they would still be making a net positive after the child goes to school for the next 13 years.
There is a lot of shit you said that I could easily tear apart, but let's just examine this little part since only it seems to be about money for you.
Here is the reality of your full time job: you have doctors appointments, sick kids, PD days, extended vacation days that non-government employees don't get, and two months of fucking summer vacation that require require somebody take time off from work because daycare doesn't cover them. Let's round it to about 50 working days, or say 1/7 of your theoretical full time paycheck. That $15080 goes to $12925. This means that your net profit amounts to $1259.
How does the spouse get to work? Usually that requires a vehicle. That vehicle will need annual registration, insurance, maintenance, and fuel. This assumes you have already paid for the vehicle and aren't making lease payments on top of that, and if that is the case you still have to think about the eventual replacement costs. So now that $1259 annual net income is reduced to somewhere between fuck-all and negative fuck-all.
Now, I don't know about your particular tax laws, but my write downs and tax credits for having a child and a stay at home wife work out to a hell of a lot more than the optimistic vehicle-less profit of $1259, and in fact probably work out to more than $3080 figure you come up with if you conveniently ignore all the costs involved.
In summation, she is costing you money by staying home with the kids: bullshit.