You cannot report your children's income on your tax return if they have 1099-B transactions. You have to file a separate tax return for each child, and report all of each child's income on the child's own tax return.
As for the 1099-DIV entries, it sounds like the children have dividends that are reported separately for each mutual fund. The payer is the individual fund, not T. Rowe Price. That's why each one has to be listed separately. That's the way the funds report the dividends to the IRS.
