In "The Son's Veto," how do different characters in Sophy's life view her with a different perspective from what she really is?
This is a difficult question because it is not at all clear from the text that the other characters do misunderstand Sophy and view her differently from what she really is. On the other hand, it is clear from the text that some judge her differently from others, but this is a different thing from how they "view" her. Our first step here is to identify what Sophy is and what she thinks she is.
What Sophy is is simple enough. She is an intelligent but unschooled woman from a small village who has natural grace and high moral conduct but who speaks with an unpolished dialect and has simple, inelegant social manners. Sophy, in keeping with the description just given, is a maid in one of the highest social families in her village of Gaymead; she is the servant of Vicar Twycott. Further, her upstanding and "spotless character" is illustrated when she scolds Sam for being irreverent on the eve of Mrs. Twycott's death.
How do Sam, Randolph, Mr. Twycott and Sophy's neighbors view her? They view her as a country woman who never received a proper education and thus talks with the lingering traces of a dialect; as a woman of high moral values who is patient and loving despite an awkwardness in society and a crippling injury. They view her the way they view her woven hair: wonderful and a work of beautiful art yet in saddening circumstances (her hair because it is limited by the night-time combing out, she because her happiness is limited to the confines of her South London existence).
These characters all view Sophy exactly as she views herself, which means that all view Sophy for exactly what she is. Now, how do they judge her? Starting with her neighbors with whom she might socialize, they judge her as someone with whom they choose not to socialize because of her unfortunate confusion over "was" and "were." Randolph judges her, now that he is old enough, through the values of his upper class education that places the distinction of gentleman above seemingly all else.
'I am ashamed of you! It will ruin me! ... It will degrade me in the eyes of all the gentlemen of England!' (Randolph)
Vicar Twycott judges her as what she was and is: his servant with a weak education, a wise head, a moral and loving heart and a person of low social standing who must be educated to do better so they might move in an acceptable social circle.
The consequences of this judgement were, however, not the same as the consequences of Sam's judgement. While Sam's judgement of Sophy led him to recognize her as a lady to whom respect was due, Twycott's judgement led him to allow their son to be openly ashamed and disrespectful of Sophy (perhaps out of disappointment she couldn't do better, certainly to discourage Randolph from adopting her ways). While Sam judged her as someone with whom socializing was eminently possible, Twycott judged Sophy as inadequate to social demands. While Sam judged her as someone he would wish to marry, Twycott, in his will, judged her as someone incapable of running financial affairs.
"If it were only myself I would do it, and gladly, though everything I possess would be lost to me by marrying again." (Sophy)
It seems from the text that Sophy and others view her in exactly the same way and for exactly what she is, yet some make judgements based on their views that differ from one another and differ from how Sophy would judge herself for herself.
she still held confused ideas on the use of 'was' and 'were,' which did not beget a respect for her among the few acquaintances she made.