So as I see it, this is the situation outlines in the letter:
Mr and Mrs Knott have 8 legitimate siblings, but unknown to Mrs Knott, Mr Knott also has an illigitimate son who he thinks is still a secret.
One of his sons, let's call him LW (letter writer) has discovered that his father had an illegitimate son (your granddad?) and has struck up a correspondence with him, hoping to introduce him to the rest of the family at some point because at this moment, he's furious at his father, Mr Knott.
He's angry at his Dad because he forced another brother, Watson, to marry a girl he had a fling with, because the girl fell pregnant before they were married. LW does not like this and describes it as "a dirty way of doing things". He's especially angry in light of the fact that his father ALSO sired an illegitimate son but never married the mother and kept it all secret.
LW is now so angry he's threatening to expose his father's secret but doesn't want to have to tell the rest of the family why he did it, which would mean exposing Watson. So his plan is to write anonymous letters, disguise his handwriting and send multiple copies to his mother and an attempt to keep himself out of it 
He's confiding in your grandfather, indicating he doesn't believe your grandfather will tell anyone and possibly also means that they haven't met (he's still an abstract to LW, can be trusted with secrets as he's not really "real"). It also indicates that this letter is probably the last of many. What it doesn't tell us is whether LW ever actually wrote to his mother and exposed his father, but I'm inclined to think not. Unfortunately, I think your father hoped that he would and that he'd be "found" by the family, as promised in the first part of LW's letter where there's a vision of them "all being together". Unfortunately, I suspect LW never wrote to his mother and never again wrote to your Grandfather, so this letter held a hope for your DGF that never came to fruition. It's desperately sad if you take this interpretation 