Living myself in Switzerland, married with a mother who stayed at home during the first 15 years of parentship, I can tell you we solved this without the government, we solved it as a team.
Just like we solved all our private matters.
The one thing we love about this country is that people here do NOT see tax as a solution to all. As a matter of fact, since this is a country with direct democracy, if we'd feel tax would be the solution we could initiate a referendum and solve that within months.
Roads, parks, power lines, communications cables, police, welfare, healthcare, sewage, electricity, clean water, healthy food, safe consumer products, clean environment, justice, protection for the vulnerable, duck wetlands, women's shelters, protection of creative works... These all cost money, and you pay for them with your taxes. Not everything goes equally to everyone, and not everything benefits everyone (by necessity), but the aggregate benefit is huge.
Forcing people to trade their future income and security to raise kids is terrible.