Hamilton Central Library have some records of the Hamilton (ducal) Estates, I know there are wages books for day labourers from around 1800 - 1820 but not sure about palace staff. There is an excellent archive at Lennoxlove House, the duke of Hamilton's stately home near Haddington but I'm not sure if there is an archivist at present. I think it used to be a wonderful lady by the name of rosalind K Marshall, I know she wrote a fantastic book called "The Days of Duchess Anne" isbn number 1-86232-111-6. worth a read although it covers an earlier period.
Below is what I think is still the email address for Hamilton Library.
hamilton.reference@southlanarkshire.gov.uk

you could also try contacting Lennoxlove, here is a link to there.
http://www.lennoxlove.com/contact

for an idea of what the palace looked like try these 2 links.
http://sites.scran.ac.uk/vhp/palace5.html

http://www.rls.org.uk/database/results.php?field=what&se...

In the period around 1855 Alexander, the 10th duke was entertaining some of the smartest and richest people in the world, including Napoleon III emperor of the French and his empress Eugene. (I think the duchess of Hamilton and Napoleon III were cousins).

good luck.