The manufacture of the shirts, intended for children under 12, is required to supply you with a certification statement with each shipment. As a retailer myself this certification statement will be stored/filed on-site. How long I don't know yet?
The dyes on the other hand will be much more difficult. You will either need to send each dye for testing or the manufacture will. In reading the law much of the responsibility falls to "manufactures." Your problem comes from the fact that a dye manufacture could possibly say ...you're problem. Instead of the reasonable assessment that dyes made for crafters need testing. Yet, they will need to supply that certification to major clothing manufactures anyway...so the dye manufacture has to test and certify it anyway.
I do see much of this along the lines of getting a MSDS, Material Safety Date Sheet, like industry was forced to years ago.
Except the thing is—lead have been prohibited in US Dyes and inks for some nigh 30 years now...