At the beginning of chapt. 13, we catch a cute glimpse of the two older boys of John & Isabella Knightley, who are returning from a visit to Uncle George at Donwell: their "healthy, glowing faces shewed all the benefit of a country run, and seemed to ensure a quick dispatch of the roast mutton and rice pudding they were hastening home for."
The previous chapter also shows a tender spot for the little Knightleys, when 8-month-old Little Emma is "happy to be danced about in her aunt's arms". Indeed, we are told that Aunt Emma chose a moment when she had the baby with her to make up with Mr Knightley, knowing that their shared love of their nieces and nephews was a strong bond.
Without straying too far into "Austenuations" territory, it seems that "Emma" is the JA novel with the most consistently sympathetic portrayal of children, and in which they figure most prominently.