Conflict brings dull stories and dull characters alive. Notice the following (Could be a children's story about a child hand raises a lamb that turns out to be intelligent and ends up saving her from danger or whatever)
Open your story with the startings of conflicts and you'll spark people's interests. We don't like reading about happy happy people with no problems- we want dirt

BUT even where there is the appearance of a lack of conflict- you can show how people sweep problems under the carpet and never discuss what is really eating away at them- this can be quite dynamic as well.
Remember to keep your characters specific traits consistant throuhgout the story until the very end where they'll 'grow' by changing- you'll want to show the domineering father as consistantly domineering & show how it affects everyone around him- The audience will be rooting for the father to finally come to realize why he is being so domineering, and to finally change.
Plot is fine, but character conflict can carry even weak plots along and make the story compelling and interesting.
"Ma, why is Pa going to the barn? Is something wrong with Lambchop?"
"You know there is something wrong with her. We discussed this at dinner."
"What's Pa gonna do? Give her some medicating?"
"Lucy! That's enough," Ma said. She whirled around and dabbed at the tears in her eyes. She knew how much Lucy loved Lambchop, and she knew that Lucy was in denial about what was going to happen. She plunked her tired aching body in the kitchen chair and began to weep.
"Don't cry, Ma. I'll fix everything," Lucy said as she ran from the house before Ma could stop her.
Lucy met her father as he stepped through the barn door with Lambchop in his arms. She shrieked in horror as she saw the limp form of her beloved lamb in her father's arms.
At the sound of Lucy's voice, Lambchop's ears perked up, and she wriggled free from John's hands. She dropped to the floor with a thud, scrambled to her feet, and ran to Lucy's side.
"Lucy, bring the lamb to me, honey."
"No! She's just ghot a cold -- that's all!" Lucy screamed.
Her father stomped his foot on the ground, and said, "That's enough. You bring that lamb to me right this instant young lady."
Lucy clung to the lambs neck. She trembled at the thoughjt of what her father planned. "I can heal her!" she said with the same defiance her father had scolded her with.
"I won't allow it! The illness she has will affect the rest of the sheep, Lucy. Now bring her here."
"Then I'll keep her seperate until she's well, father." And with that Lucy sprang from the ground, and she and Lambchop ran down the path toward her secret spot in the woods.
~~Here we've given the father, and mother the tough love characteristics that fail to see things on the level of children.
You can show in later details that the mother thinks that because she had to grow up so early in life and 'toughen' up, that everyone should have to- but deep down, she acts this way (Even though we see her crying) to hide the fact that she is someone who always gives in to others emotionally.
You can later show the father only acts the way he does because he is stressed about losing the farm, but deep down, it's more than that- he subconsciously fears he's losing more than the farm, he fears he's lost his family as result of long hours and no time for them. (This can bring up wonderful conflicts throughout the story as the couple squabble and blame each other for their daughter running away)
You can also show the daughter growing up- maturing, and trying to become something other than what her mother was -- a give-in. She later finds out just how much her mother has sacrificed for her, and realizes that there is no other person she woul wish to emulate.
Lots of character possibilities in something like this.