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"And so it is!" said the child [Pearl]. "And, mother, he has his hand over his heart! Is it because, when the minister wrote his name in the book, the Black Man set his mark in that place? But why does he not wear it outside his bosom, as thou dost, mother?" (16.32)
As bad as it is to live your life as a hypocrite, it's even worse when your kids figure it out. This is the "Do as I say, not as I do" school of parenting, and it works just about as well as it always does. (Not very.)
"Doth he love us?" said Pearl, looking up with acute intelligence into her mother's face. "Will he go back with us, hand in hand, we three together, into the town?"
"Not now, dear child," answered Hester. "But in days to come he will walk hand in hand with us. We will have a home and fireside of our own; and thou shalt sit upon his knee; and he will teach thee many things, and love thee dearly. Thou wilt love him; wilt thou not?"
"And will he always keep his hand over his heart?" inquired Pearl. (19.33-37)
Pearl answers her mom's question, "Will you love Dimmesdale?" by saying, essentially, "Will he still be a hypocrite?" She can't love him while he's living a lie—and the moment he confesses, she acknowledges him as a father. Too bad that he's literally dying when he does it.
"What a strange, sad man is he!" said the child, as if speaking partly to herself. "In the dark night-time, he calls us to him, and holds thy hand and mine, as when we stood with him on the scaffold yonder! And in the deep forest, where only the old trees can hear, and the strip of sky see it, he talks with thee, sitting on a heap of moss! And he kisses my forehead, too, so that the little brook would hardly wash it off! But, here, in the sunny day, and among all the people, he knows us not; nor must we know him! A strange, sad man is he, with his hand always over his heart!" (21.10-12)
Yeah, it is weird that Dimmesdale will only acknowledge his lover and child in the dark forest—weird and sad. But not quite sad enough for us to feel sorry for him, since there's an easy fix.