No. Supplemental Security Income (SSI) is excludable from gross income. However, for purposes of claiming a dependency exemption, you have to take government benefits into account in determining support. You can claim an exemption for a qualifying child, such as yours, as long as the child does not provide more than half of his or her own support. Government benefits, such as SSI, are treated as provided by a third party (the government) to the dependent.
A mutual-fund distribution allocated to gains realized on the sale of fund portfolio assets. You report the distribution as long-term capital gain even if you held the fund shares short term.