Do you see connections in writing styles between Louisa May Alcott and Henry Wadsworth Longfellow?

Longfellow and Alcott were both New England writers; Longfellow was born in Maine and Alcott lived in Concord, Massachusetts. Their lives overlapped somewhat; Longfellow was 26 years older than Alcott but they died about six years apart. They were both important 19th century American authors. Along with their biographical similarities, they share similarities in their writing. 

Alcott's best known book is Little Women, which remains a classic in children's literature. It is the fictionalized, idealized story of Alcott and her three sisters as they grew up. Alcott's actual childhood had been difficult, since her father had a hard time keeping a teaching job due to his radical ideas of education. In fact, Alcott wrote Little Women as a way to help the family's finances. 

As a romanticized portrayal of childhood, Little Women shares characteristics with Longfellow's poetry, particularly his poetry about children. Here is the opening of Longfellow's The Children's Hour:

Between the dark and the daylight,
When the night is beginning to lower,
Comes a pause in the day's occupations,
That is known as the Children's Hour.

I hear in the chamber above me
The patter of little feet,
The sound of a door that is opened,
And voices soft and sweet.

From my study I see in the lamplight,
Descending the broad hall stair,
Grave Alice, and laughing Allegra,
And Edith with golden hair.

Here is the first description of the characters in Little Women:

Margaret, the eldest of the four, was sixteen, and very pretty, being plump and fair, with large eyes, plenty of soft, brown hair, a sweet mouth, and white hands, of which she was rather vain. Fifteen-year-old Jo was very tall, thin, and brown, and reminded one of a colt; for she never seemed to know what to do with her long limbs, which were [Pg 5] very much in her way. She had a decided mouth, a comical nose, and sharp, gray eyes, which appeared to see everything, and were by turns fierce, funny, or thoughtful. Her long, thick hair was her one beauty; but it was usually bundled into a net, to be out of her way. Round shoulders had Jo, big hands and feet, a fly-away look to her clothes, and the uncomfortable appearance of a girl who was rapidly shooting up into a woman, and didn't like it. Elizabeth—or Beth, as every one called her—was a rosy, smooth-haired, bright-eyed girl of thirteen, with a shy manner, a timid voice, and a peaceful expression, which was seldom disturbed. Her father called her "Little Tranquillity," and the name suited her excellently; for she seemed to live in a happy world of her own, only venturing out to meet the few whom she trusted and loved. Amy, though the youngest, was a most important person,—in her own opinion at least. A regular snow-maiden, with blue eyes, and yellow hair, curling on her shoulders, pale and slender, and always carrying herself like a young lady mindful of her manners. What the characters of the four sisters were we will leave to be found out.

The reality of children and young ladies is more complex than this portrayal which leaves out the mixed feelings everyone has. While Little Women discusses the poverty of the Alcott family, it is a gentile poverty and not the grinding poverty portrayed in, for example, Charles Dickens's novels. Likewise, Longfellow's description of his children is similar to that of Alcott. 

Both Alcott and Longfellow portrayed misbehavior of children in their works; Alcott's novel depicts Jo's struggles. Longfellow wrote:

There was a little girl,
Who had a little curl,
Right in the middle of her forehead.
When she was good,
She was very good indeed,
But when she was bad she was horrid.

Still, these works glance over the top of misbehavior, which gives them a romanticized feel. While these two authors differed somewhat in age and also in gender, they shared a sense of depicting only what might be acceptable to their readers about the people they portrayed.