I have 2 kids with different fathers. I do not receive child support for either one. My younger son is disabled and I receive SSI for him. If I take his father to court for child support, will they lower the SSI or lower his child support because I receive SSI? And if I take my other sons (the one that is not disabled) dad to court for child support will they lower my SSI?

They can consider the SSI as part of the household income so it may have some effect as to how much you receive. The SSI is separate from your income and any child support received will not be counted against it.