How did the Stevenses act towards the Worthens in Lyddie?How was Lyddie's relation with them different from her mother's?

Lyddie's mother does not like the Stevens family because they are Quakers, but they are good neighbors.

The Stevens family is neighborly to the Worthens, even though Lyddie’s mother wants to avoid the Stevenses because they are Quakers.  They let Lyddie breed her cow to their bull.  When Lyddie comes back to sell the calf, Mr. Stevens is upset that he did not realize that the children were there alone.  He would have helped them...

Lyddie's mother does not like the Stevens family because they are Quakers, but they are good neighbors.

The Stevens family is neighborly to the Worthens, even though Lyddie’s mother wants to avoid the Stevenses because they are Quakers.  They let Lyddie breed her cow to their bull.  When Lyddie comes back to sell the calf, Mr. Stevens is upset that he did not realize that the children were there alone.  He would have helped them if he knew. 

Charlie, in fact, wanted Lyddie to ask for help, even if their mother would not approve.  She left the two of them there on their own. 

He glanced about to make sure his mother wasn't in hearing distance. "You mustn't be afraid to go down and ask the Quaker Stevens for help, Lyddie. They mean to be good neighbors to us, no matter what Mama says." (Ch. 1) 

Their mother was strictly religious and thought the Quakers were strange.  She did not approve of their religion, and therefore avoided them.  It was not uncommon for people to discriminate against Quakers because they acted, dressed, and worshiped differently.

Lyddie used the cow because she needed to, but she did not want to be beholden to anyone.  She was able to sell the calf back to Mr. Stevens, who agreed because he knew the children were desperate.  He even invited the children in for lunch. 

He invited them in to complete their business transaction and, before they were done, they found themselves eating a hearty noon dinner with the family. (Ch. 2) 

The incident with the Stevens farm shows how independent Lyddie is.  She wants to be able to do things on her own.  She is forward thinking, breeding the cow so there is a calf and milk and dairy products.  Her mother is not right in the head, and never thinks about any of it.

Quaker Stevens buys the farm, and his son Luke Stevens even asks Lyddie to marry him. She does not accept, again wanting to be independent.  She also barely knows him.