Hello Hayley. Around that date, there was a Dr. Barnardo's Home , 'Dane Court,'
12, St. Peter's Road, Parkstone. This appears to be the most likely place if they were sent to a home in Poole but there was also a Hants & Dorset Babies Home, 'Fairholme,' 14, Commercial Road, Parkstone and a Parkstone Refuge at St. Faith's, Bridle Path, Upper Parkstone.
However, if they were sent to a home in Bournemouth then there are several other possibilities - the most likely one being the National Sunday School Union Children's Convalescent Home. They had a house at 11, Derby Road and one at 'Beardwood,' 19, Stourwood Avenue, West Southbourne. The later home was aquired to replace one that had to be evacuated from Clacton ( it was full to capacity as well).
Bournemouth Borough had a home at 16, Stourwood Avenue, West Southbourne (Evacuees Sick Bay for Children). Hollybrook Children's Home, 6, Boundary Road, Ensbury Park is another possibility and there were homes at St. Gabriel's, St. Clement's Road, Boscombe (for convalescent children) & one at Victoria House, Alumhurst Road but this was for crippled children.
All the best with your research
Morten