It took Hasbro a very long time, but finally the Rainbow Ponies were to have baby ponies. Or you'd think so, from the set name. but in actual fact the four little ponies Hasbro introduced have quite seperate identities from anything that went before. It's possible to draw tenuous resemblances between Windy and Baby Rainribbon, Sunlight and Baby Sunribbon and even more tenuous ones between Starshine and Baby Starbow, but there is no explaining Baby Bright Bow in this manner. So it seems that the Rainbow Babies were never intended to be children for the original Rainbow Ponies (a shame, in my view.)
The Rainbow Baby Ponies, according to their UK backcards and the comics lived in Rainbow Mountain, under the guardianship of the Rainbow Curl Ponies, one presumes. Rainribbon got her name because she always called rainbows 'rainribbons', I remember that most clearly.
Important to note is that there exists a version of baby Starbow with a blue streak in her mane instead of a purple one. She was not sold in the UK but I believe she was sold in North America. I'd like to thank Erica for the picture to the left of blue streaked Baby Starbow  :)
On a personal collection pride note - Baby Rainribbon was my first ever baby unicorn as a kid ;) Sorry, had to share that :D