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.
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!