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Hello hbar  !
I hope my honest review will be helpful to you during future edits. Keep in mind these are my personal suggestions based on my knowledge, beliefs, and limitations. Please accept only those which might make your work stronger.
You asked that this review cover punctuation and clarity, so I'll do my best.
First Impressions:
You've made me miss the farm I lived on as a child. Your description of the "arrival" surrounded me, transporting me into your world. You're an expert at setting the scene and filling it with ambiance. 
Punctuation:
Realizing your weak areas is half the battle! I'll give some general rules, but I'm not a grammar expert. I'm also unsure if you are using sentence fragments on purpose as part of your style, but I'll point them out just in case.
There's some punctuation missing here. Descriptions of people should be offset with commas.
Lizzie their eldest now twenty-one at his left and
Lizzie, their eldest, now twenty-one, at his left (?)
I won't attempt to punctuate the entire sentence. *I* would split it into two sentences to get around the semicolon/colon issue.
“Oh look at you Jack,
“Oh, look at you, Jack,
 Dialogue tags:
In general, if the verb is said/asked/etc., link the dialogue tag to the dialogue with a comma.
It’s Jack everybody.” Jeremiah yelled
It's Jack everybody," Jeremiah yelled
“Well ask him in Jeremiah.” Eleanor exclaimed
“Well, ask him in, Jeremiah,” Eleanor exclaimed
If the verb is a non-speaking action, such as smiling, walking, or beaming, you can create a separate sentence, which might free up your possibilities.
Jack looked at his feet, “No sir, no I haven’t.”
Jack looked at his feet. “No sir. No, I haven’t.”
Perhaps this pause could be enhanced by starting a new sentence?
to visit my folks,” he paused, adding with quiet emphasis “I made peace with my dad
to vist my folks." He paused, adding with quiet emphasis, “I made peace with my dad
Sentence fragments/comma splices/etc. (ignoring style issues):
waist, it matched
waist; it matched
(A semicolon joins independent clauses.)
would be seated; watching her family
would be seated, watching her family
{The second clause is not independent; it needs a comma.)
A tire swing hanging from a limb just visible.
(The gerund form (ing) makes this an incomplete sentence.)
Work boots on his feet,
You may wish to condense/combine the description here and add a verb on which to hang the phrases.
resumed eating. Not meeting Jack’s eyes.
resumed eating, not meeting Jack’s eyes.
Warmth.... Fried chicken....
Consider combining the clauses in a different way to put the description and his reaction in separate sentences:
"Warmth seeped from the open door, along with the smell of fried chicken, dill and potatoes, and baked apples. Frank and Eleanor...."
their supper. Except Thomas, a solid stream
their supper, except Thomas. A solid stream...issued
or
their supper. Except Thomas--a solid stream...issued
Other:
sweat stained hat = sweat-stained
Clarity/Flow:
I believe your opening paragraph is a good hook. There's a homecoming for the main character, and we sense his uncertainty about whether he'll be welcomed.
The gravel crunched beneath his boots as he walked the road to his unknown destiny. 
Excellent! What do you think of putting the character's name in the first paragraph, or even the first sentence? It might help the reader connect to him as a person. That way, when the other people are introduced in the fourth paragraph we have a good idea who Jack is.
Jack watched absorbedly
I'm not sure you need the adverb. You do a great job of showing how Jack watched her every move.
The home was visible
The house was surrounded
limb just visible.
You know what I'm going to say here, right? Passive voice puts the emphasis on the house, which is fine if that is what you wish. Consider giving the information through Jack's eyes. I think it might work, especially considering this gem of a sentence:
He looked at the home, not moving, inner conflict turning his feet to stone.
You could even leave out "he worried", because you give internal dialogue.
Fear absorbed him, leaving him unable to move. 
Excellent!
The Cleef’s had taken him on as a hired hand. He had walked....
This seems backwards. Consider switching these sentences and/or combining them.
"He walked onto the Cleef ranch looking for work."
Jack hoped they would welcome him again.
Consider starting another paragraph here, since the first portion describes when he worked for them, and the remainder is more about his feelings. What do you think of putting this sentence at the end of the paragraph? It might be a strong closing and a segue back to the present.
Description:
I love the setup! The overheard discussion, the tire swing, and the sights and smells of the house are great details that say "home" to a weary traveler. Perhaps describing Jack's feelings in more detail might flesh this out. For example:
He stood nervously before the front porch.
This is a moment of tension. Is there a way to show how nervous he is? Sometimes a tiny detail adds just the right amount of emotion to a story. Perhaps his hands got hot despite the cold temperature, he sighed, or he crunched his hat in his hands--a physical symbol to reinforce his trepidation.
Standing off the porch
I'm not sure if this is a regional saying, but normally we say "standing on the porch", or "beside the porch". It took me out of the story for a second to translate. You could describe where "off" is. Perhaps he had one foot on the first step? That would show he's hesitant, too.
Eleanor gave him an appraising, worried look
This is a great description of a mom's action, and an opportunity to flesh out some details if you want. How does she give an appraising, worried, look? My mom would probably look me up and down, frown, then give a fake smile to cover her worry, and pat me on the back.
He watched only Lizzie....
I love the description here. It shows exactly what it is about Lizzie he admires.
Plot:
The plot is good. The ending kind of left me hanging, which is probably your intent. We don't need to know whether he gets the girl or not, but it would be nice to know what he thinks about the situation at the end. Does the fact that his woman has a new beau leave him resigned, or is he determined to win her back? My personal preference as a reader for nice, tidy endings makes me wish for a subtle clue as to whether this is a tragic situation or a new beginning.
“Stay here, Jeremiah,” Frank said softly.
A subtle authority shows in this line. Frank is a wonderful character. You show his love for the young man well in his actions (the handshake), in his dialogue, and in the unspoken places between action.
On the other hand, Lizzie seemed an ethereal love, almost an archetype. To me, the story was more about the concept of family than about romance. You've conveyed this well, although you may wish to enhance the ending to make it more clear.
Favorite line/s:
He could hear indistinct supper conversation interspersed with laughter.
This short sentence really painted the ambiance for me. Without any description, I heard clanking dishes and people talking in my head. Awesome!
Overall:
Complex emotions and motivations in this piece made it an absolute joy to read. You have a unique insight into your character's souls which gives a depth to the story.
I may not always understand the subtleties of your work, but I'm always available for questions, comments, accusations, and re-rating. 
Write on!
In gratitude,
Kimchi
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Merry Christmas! 
The more I review, the more elusive a 5 becomes for me personally as well as those I review. A 4.5 is darn close to perfect--leaving the .5 open. Here are possible reasons:
I love the premise of your story and the anticipation of mother and daughter finding each other. I'm waiting for Chapter 2--I just know there will be action. Keep writing! 
Love this image!
