Hello JohnLFC,
It looks to me as if the information is all a bit tenuous with nothing very certain held at all. The problem with things passed down the family is that often they have no factual basis. I have come across this in my own research, where one gt grandmother in particular, told my mother all sorts of interesting family history, nearly all of which has been proved to be untrue.
Unless there is some definite factual basis for the stories that have been passed down, I would be inclined to be very wary of these.
My thought on the name change is that Albert was illegitimate as another person has suggested. He would have had his birth registered, maybe baptised, in his mother's name, so he could have changed his name to Parker to acknowledge his father.
Unless you can find something to show Thomas served in the Hussars, again be wary of this information. This tends to be supported by the fact that there is no official record to verify the details.
I think we may be looking at needles and haystacks with this one.
Bear in mind that in the years you are talking about, Shoreham on Sea would have been a tiny fishing village and port. Most of the town that exists today was built up much later on.
My thought would be to try and identify details for Thomas Parker if possible. We know he died pre 1920, so have you tried to find a death for him? That would be a certainty but not easy to be sure as it is such a common name. We know he was alive in 1883, so died between then and 1920. It is possible that he was married to another at the time Albert was born.
It might be worth contacting the Sussex Family History Group to see if they can shed any light on this and the connection to Shoreham, Sussex.
http://www.sfhg.org.uk/The search for Albert's mother will be a very time consuming task indeed. It could mean looking at all the births registered for Albert in 1883 if you are sure he was born in that year. Does anyone know his birthday date?
Jo.
