Ah, Aunt Polly:  tenderhearted, loving, but usually misguided Aunt Polly.  She is the caretaker of Tom Sawyer (after Polly's sister, Tom's mother, died) and is always desperate to understand Tom.  Her favorite charge, however, is Tom's brother, Sid.  Aunt Polly is always asking Tom to look to Sid in regards to how to behave. 

Aunt Polly is usually seen either quoting scripture, asking Tom to be more like Sid, warning Tom to be more civilized, or hitting Tom over the head withe her thimble.  Tom is not a fan of this type of treatment, so for all of Aunt Polly's tries, ... she fails to win Tom over. 

Aunt Polly is also the glue that cements the rivalry between Sid and Tom as well.  Polly is always trying to figure out Tom's doings.  Tom is always trying to give her some kind of convoluted explanation (and usually succeeds).  Sid prides himself in helping Polly note the inaccuracies in Tom's descriptions.  (Thus, Tom gets another thump with the thimble.)  In my opinion, Aunt Polly's relationship with Tom is summed up here:

In another moment he was flying down the street with his pail and a tingling rear, Tom was whitewashing with vigor, and Aunt Polly was retiring from the field with a slipper in her hand and triumph in her eye.

But of course, we KNOW what happens in regards to Tom's whitewashing the fence.  Aunt Polly never seems to have the upper hand!

Tom and Sid's mother has died and Aunt Polly (their mother's sister) brought them into her home to raise them. Aunt Polly is loving and sweet, but apparently she has difficulties raising two boys. Aunt Polly tries hard to steer Tom in the right direction, giving him advice on how to behave and administering punishment when he steps out of line, such as making him whitewash the fence.

Aunt Polly unwittingly plays into the rivalry between Tom and Sid, holding Sid up as a model "good boy" when she chastises Tom. Her well-meaning efforts to mold Tom's behavior only serve to intensify the problem between the two boys.

Aunt Polly also knows that Tom is prone to do the wrong thing, and she tries to set traps to be able to catch him, such as stitching his shirt collar with a particular color thread in case he ditches school to go swimming. Of course, Tom is usually one step ahead and always can figure out how to get out of a punishment.

What is the character of Aunt Polly's realationship to Tom in The Adventures of Tom Sawyer?

Aunt Polly is Tom Sawyer's kind-hearted guardian. She is the sister to the late mother of Tom and Sid.

Aunt Polly wants to raise Tom right, but the high-energy boy is always into some sort of mischief and almost too much of a handful for her. Her chief dilemma is that she likes him too much to want to punish him, and yet she knows it is wrong to let him get away with his hijinks. As she puts it,

Every time I let him off, my conscience does hurt me so, and every time I hit him my old heart most breaks.

Aunt Polly speaks in the dialect of Hannibal, Missouri, and her life is guided by a mixture of religious and folk wisdom. She hits Tom on the head sometimes with her thimble, but mostly, Tom is able to get around her and do what he wants. Sometimes she tries to use her wits or a little well-intended manipulation to get him to behave, but most of the time, this fails. As the narrator says,

Like many other simple hearted souls, it was her pet vanity to believe she was endowed with a talent for dark and mysterious diplomacy.

Aunt Polly is also interested in patent medicines and quack medical therapies. Often the medicines she gives Tom simply make him so drunk that he falls "on the floor expiring with laughter."

What is the character of Aunt Polly's realationship to Tom in The Adventures of Tom Sawyer?

Tom’s Aunt Polly is his mother’s sister.  She takes care of Tom and his brother Sid.  She loves Tom very much, which is why she does not want to punish him when she catches him doing wrong.

He's full of the Old Scratch, but laws-a-me! he's my own dead sister's boy, poor thing, and I ain't got the heart to lash him, somehow. (ch 1)

Even though he is a troublemaker, Aunt Polly knows that Tom’s heart is in the right place.  He does not feel bad about tricking people and trying to get out of work or school, but he does feel bad about giving his aunt frets.  They have a good relationship, and Tom does not seem to regret having no mother.  She still feels sorry for him though, and makes allowances for him because of it.