It seems like there is this assumption that these parents are together and sitting down to make rational decisions. I am not sure if the encouragement and education will deter younger people from having more children.
Further, laws actually support women in having multiple children given the child support and welfare laws. Essentially, a woman can make a living by producing children. Even with the education what is to deter her from producing more children given that she doesn't have to work for the next 20 years of her life?
I agree completely that men and women should have easy access to birth control and abortion clinics need be. But this still doesn't address the issue posited above.
My proposal would be to address welfare laws in culmination with education and easy affordable access to birth control/abortion clinics. Those receiving welfare should receive welfare as any employee receives a check. You get paid for your services. Those who receive welfare have two responsibilities: household financial manger, that must conform to guidelines to ensure the child(ren) receive adequate care, and they must perform civil services such as public works projects (clean-up, garbage, infrastructure improvement) or some other type of work in exchange for receiving funds. Essentially, you give a person both a job and money rather than just money.
This, I believe would discourage women that seek to produce children as a career. Thus, lowering the birth rate among the indigent. Again, I am not saying that all or most women do this. Even men and women who do receive welfare did not choose to do so. They may have lost a job or spouse and cannot afford to provide care for children. Nevertheless, providing these people a job and pay (welfare), is both a helping hand and act of self-reliance, and therefore this form of welfare would not feel like a "hand-out", and rather, give a person a sense of pride.
On the other hand, I know of several families (both single-parent or nuclear) with low-income that work and provide adequate care for their children. In this case, the parent(s) need not be penalized, since they are exercising personal responsibility without costing the state, and other hard-working tax payers for raising their children.
Therefore, the laws need to be amended to fit this principle:
"The number of children one can have should be limited to the number of children the parents are willing and able to provide adequate care for"...and if circumstances change, the government can provide you a temporary job to supplement job loss or unemployment to parent(s).