Oh what a wonderful topic Beth full or many different possibilities!!!!! Like Torkel I also think the lady next to the Kaiser is not Queen Alexandra because the other three people are instantly recognisable as the persons depicted but this lady looks too young to be Alexandra. One thing Im also finding odd is the placement of the guests at the table. The two sovereign couples should be sitting side by side (as we often see now at state banquets at Buckingham palace) or opposite each other (as is done at Windsor now). When Queen MAry & King George V visited berlin for the Kaiser's daughter's wedding they were seated as the premier guests on a long table opposite each other with the Kaiser and Kaiserin.
Anyhow we are probably veering wayyyy off topic but I have another observation i.e. in the illustration of the ball isn't the lady dancing at the very front also wearing the tiara which we think is the amethyst tiara??
I would hazard a guess and say that the lady standing next to the Kaiser in the Illustration is Winifred Cavendish-Bentick, The Duchess of Portland who was Mistress of robes to Queen Alexandra and is likely to have attended the Queen during the state visit. The tiara on her head being the Portland diamond tiara.