How does Hester feel when she saw Dimmesdale marching in the procession in The Scarlet Letter?

I assume you are referring to Chapter 3 of the novel, when
Hester Prynne and Pearl are being "displayed" as punishment for her sin, and Arthur
Dimmesdale is forced to try and persuade her to reveal the name of the father of her
child. What is interesting about his appeal is the impact it has on the audience. For we
are told that it was so powerful the audience expected Hester Prynne to respond straight
away or for the father to be compelled to reveal
himself:

So
powerful seemed the minister's appeal, that the people could not believe but that Hester
Prynne would speak out the guilty name; or else that the guilty one himself, in whatever
high or lowly place he stood, would be drawn forth by an inward and inevitable
necessity, and compelled to ascend the
scaffold.

However, in spite
of the power of Dimmesdale's appeal, Hester Prynne is unmoved, merely shaking her head
in response to his eloquence. What is important to note, however, is that when she is
shouted at by the Reverend Wilson and exhorted to reveal the name, it is Arthur
Dimmesdale who she looks at when she responds, and not anyone
else:

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"Never!" replied Hester Prynne, looking, not at
Mr. Wilson, but into the deep and troubled eyes of the younger clergyman. "It is too
deeply branded. Ye cannot take it off. And would that I might endure his agony, as well
as mine!"

Of course, if you
have read the book, you will know that it is actually Dimmesdale who is the father of
Pearl, and thus his presence at this scene gives Hester Prynne the opportunity to
confirm to him that his secret is safe with her. Note, too, the manner of her response
which likewise establishes the tremendous love that she has for him - she wants to
suffer alone and would "endure his agony" in addition to her own
suffering.