I don't have as good of an answer for reducing children. It would probably be best to work on reducing the number of children by providing easier access to birth control.
You're completely and utterly ignoring the fact that raising children, especially multiple ones, is an extremely difficult task, even for two people. I know of very few people who would opt to do it themselves, even if the financial incentives to do so were worth it (they aren't even close).
I just want to point out there are a lot of poor women raising significant numbers of children. The woman next to my mom has 5-7 (it's hard to tell, and she just had a new one). They father (of some of them) is around a little, but mostly not around. And it looks like there are several fathers. Yes, raising children well is hard, but I would not describe what this woman does as difficult. Older kids are raising the younger ones, etc, etc.
So, I would definitely disagree with your assertion.
That's not really a good idea. I know my godson's parents, and if they getting assistance was reliant on getting married, they would end up killing each other.
"If we changed government assistance to encourage parents to have less children they would be better able to take care of the ones they have."
How, exactly would you do this? And do it without punishing the kids by leaving their parents with even fewer resources?