Thanks for the helpful hints. I will follow them up and get back to you. I might be able to give you more to go on, should you be able to check my folks out at the Records Office (for which I would be extremely grateful).
Re Sandhurst, my great-grandfather built a house and called it Sandhurst. An elderly relative (now deceased) told me it was named after the place the family came from in England. The only Sandhurst I knew of then was where the military academy is (?Cambridgeshire), and as I knew the family was from Glos. I dismissed it, especially as my mother has a very different story of how the house got its name. However, when I found a William Beard on the IGI born at the right time at Sandhurst, Gls. I thought I might be on to something. I also note from the maps that Sandhurst is quite close to both Cheltenham and Glocester City, where two of the children were born.
I will have to get a handle on the other place names you mentioned. Many thanks for your help.