It was actually the Bolsheviks who sent the trunks to the Family. It was sort of a publicity stunt, to say "yeah we sent everything that was left". The truth was that the trunks held nothing of value at all. Frayed table napkins and tablecloths, towels, clothing, broken bits of china.
I spoke with Bob again about the clothes. They didn't save "everything", just the expensive and fancy couture, and Nicholas' and Alexei's clothes. The girls' "everyday" clothes were sold at used clothing shops in Petrograd. Don't forget, they were hopelessly out of date and fashion by the 1920s, and the Civil War had made clothing quite scarce. So, shoes, skirts, underwear, socks, etc. were needed by "the people" and were not seen as necessary for the "museum" mission of the AP.