My ex and I still live in the same home. He helps pay for very little of the expenses and we have two children under the age of two. I bring home only $300 a week, and he brings home $800 a week. Is there a way to get child support to help fill the need of the children even with him in the household, as he does not support them now?

You can try but him living in the household will make it an uphill battle.

Who's name is on the deed/lease? If it is his name or both your names it basically won't happen. If it is just in your name then you need to draw up some sort of contract with him so that the bills are split equally between the two of you for rent and utilities first then you can try it in court.