It is still a bit mysterious why the Osborne family (originally from south Somerset) moved to Bournemouth for work before heading back to the Welsh valleys. Perhaps their original move to Bargoed didn’t work out, and through relations they had heard that Bournemouth needed labourers for its fast development (late 1870s)? They were there perhaps about 1877 to 1880, as the 1881 census shows them in the Rhondda, where they stay.
Amelia’s birth certificate shows she was born at Princess Road, Springbourne. This no longer exists, and appears to have been where Cleveland Road, Bournemouth is now. Wikipedia gives a little info on Springbourne as a suburb of Bournemouth.
The spasmodic family connection with the town has continued, such as for leisure or union conferences. Most tragically this saw the death of Amelia’s granddaughter Irene O’Brien in 1970 while on holiday, staying less than a mile from Amelia’s birthplace.
Streets of Bournemouth website is in archive but still some useful amterial on history etc.