Hello David

I had not heard of the House Beautiful Convalescence Home before. My personal local knowledge mainly concerns Boscombe, Pokesdown and Southbourne...Derby Road is just a little over the border However I've done a little searching on the net and found an old British Medical Journal article which mentions the home - http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2444295/pdf/brmedj07142-0029.pdf

There is also a mention of it in "Bournemouth 1810-1910, the history of a modern health and pleasure resort" by Charles Henry Mate:-
"The " House Beautiful " is another Institution for London children - established in connection with the Sunday School Union. It is, perhaps, more in the nature of a holiday home than a hospital, but without question its work is a beneficent one."

I don't know specifically what kind of information you are seeking about the home but I should be able to locate it on the 1901 census for you, which would give the details of staff and patients there at that time, if that would be of any interest to you?

Regards, Lisa