I am leaning toward it being the same Edward with perhaps the first two girls being Rosa's children, some of the boys being Edward's and then some children being theirs together. OR Rosa and Alicia/Alice are the same person.
There was a Mary Charlotte RHEESE who married in Queensland in 1879 to Frederick MORCOM. When she died in NSW in 1935 her father was given as Edward (no mother named) and I saw that her death notice named two of her daughters as Alice and Rose. Looking at births in Queensland we find that the birth of the daughter Rose was registered in 1882 as 'Rosa Alicia'. Is she Rosa Letitia's sister?
Did you end up getting your Rosa Letitia's marriage cert to see who she named as her parents? They are a lot cheaper these days and can be downloaded online as an image. I would also want Mary Charlotte's marriage cert - I do think she is Rosa's sister. I know it gets a bit expensive, but sometimes documentation is the only way to find the bits of the puzzle.
I would also get the 1864 NSW birth of Edward RHEESE to Edward and Alicia, and the 1877 death of George RHEESE as listed in my previous post. It is a big punt, but if they are connected it could open lots of doors for you. Transcriptions are much cheaper that official certs in NSW and transcription agents are listed on the NSW BDM website under the 'Family History' link. They often have special deals around Christmas time or maybe you could put them on your Christmas list :)
Debra