I am not sure how having policies in place to make raising children easier (affordable daycare, family leave etc.) translates into the government telling us how to raise children. That makes no sense.
As far as people without children feeling it's unfair for any tax revenue to go to helping families, look at it this way. Raising children is expensive and time consuming and usually makes it harder to have a high-powered career. There are a lot of sacrifices involved in raising children. These children we raise will be the citizens of tomorrow who will be running this country, while supporting social security medicare, our armed forces etc. Everyone benefits from having children raised well. So I don't think it's too much to ask the tax payers to chip in a little when the children are small. You will benefit from these children later.