"...she was so overcome
of what lay..." ("by" or "with" would be a better word choice in this sentence.)
You are missing a period (.) at the end of the first paragraph.
"An intake of breath..." (If you wanted this to be more powerful, you may consider "Her sharp intake" or "A sharp intake", something like that)
when you are writing dialogue you should be using quotation marks at the beginning and end (") instead of (').
This sentence makes no sense written as it is. I will show needed corrections within the sentence: "Watching
, the train flew by
and she once again found herself..." There is also an extra space between the words "again" and "found" that you need to remove.
"...countryside consuming her; her plans of hiring a car to meet Alec flew..." In the area I am showing, it would be better to get rid of the semicolon (;) and use a period (.) and begin a new sentence with "Her plans..."
"A walk in the tranquil Irish countryside, inspiration is exactly what was needed." (Doesn't quite flow. Consider the word "this" before inspiration, or somehow phrasing that thought more clearly for the reader.)
"that dream was commonly known
around her peers." (Did you mean among?)
In this sentence you need to refer to both parents in the same way, either with or without the s at the end of their reference (I personally would drop the "s" on mothers): "stubbornness was that of her
mothers, and her patience and kindness of her
father."
The way the words grandmother and grandfather are used in the following sentence, they do not need to be capitalized, as it is making reference to them, not using the words as names (like if you were calling to them): "and her beloved
Grandfather and
Grandmother""
It would be good to give more vivid description to the countryside to let your readers SEE it for themselves as she does. Not only be told of her reaction to what she sees. This is how you can really bring your story to life and engage the reader. Tell about sights, sound, smells, touch (she felt the winds in her hair), taste (if applicable). Engage the senses, thus giving the reader a feeling of being there with you. Show these things.
It would also help to consider some different word choices in a few areas where The words do not flow well. Consider tightening the longer sentences and using more powerful wording to really grab your readers!
On a last note, punctuation is NOT my strongest point, although I am working to improve it. Some punctuation didn't seem right in this, but without feeling strong in that area, I do not want to ill-advise you. Maybe copy this story, and paste it into a free online grammar and punctuation checker. I like paperrater.com Also know, I still struggle myself with many of the areas of suggestion above. It is by receiving thoughtful and thorough reviews, that I am able to improve. Try reading your story out loud, and that may help you with identifying points of weakness. I do this, and usually I will catch things that reading it silently doesn't allow me to notice as easily.