Hello! Thank you for sharing your writing, it's difficult to feedback online as criticism meant constructively can come across badly, but I want you to know that none of my comments are meant sarcastically or nastily! I'd love to see more of this story, I'd like to know what happens to this little family 
The house had the air of something resurrected;
What did you want that to mean?
softly decaying around its edges despite the fix-up job.
What fix up job? 'The' suggests we know about some kind of renovation. Maybe 'despite a recent and somewhat unsuccesful fix-up job' or something.
Windows stared down like lifeless eyes which saw nothing and everything.
Bit existential for a Wednesday, decidedly more profound than the rest of the excerpt.
Overgrown ivy crawled down one side of its red-brick exterior, curling around its top windows like matted hair.
That is a really lovely metaphor
Framed in an artificial summer’s day,
What is an artificial summer's day?
it was still and silent, the surroundings stifling in their perfection.
Why were they so perfect? So far the house sounds like a dump.
And yet, Kate knew it was home.
GAH! Surprise character! Who is she? What's she like? I was just getting my head round the house. Characters are easier to picture and relate to when they're introduced properly in the third person.
She stood now,
Why, what was she doing before?
staring up at their new home from the driveway, shielding her eyes from the searing sunlight, ignoring the shadows lurking around its edges.
Can this sentence be broken up a bit? It makes several points but it's long. Also 'staring' isn't a particularly flattering sounding thing to be doing.
A proud smile crossed her face. To her, the house was perfect.
Naww, Kate
Too perfect, her husband Charlie had said when they first viewed it, clutching glossy brochures in their hand as they hung on every over-enthusiastic word of their estate agent.
hands - there's more than one hand involved. How did Charlie say it, was he annoyed, suspicious, in awe, excited?
The fresh white paint on the window sills hid the crumbling mortar around its edges, the neat gravel of the driveway covered the mud tracks that had laid there before and the symmetrical red brick chimneys on either side of the roof drew her eye away from the dappled green and black moss poking from beneath new roof tiles.
Nice!
Each perfect thing about the house had been framed in the warm summer’s day which had appeared from nowhere following their two hour drive through torrential autumn rain for their first and only viewing.
But the house was a dump, mixed messages, slightly confusing time jump from viewing to moving day, took a couple of reads.
‘Charlie, can you grab the last two bags from the boot? I’ll get Lottie.’
Who is Lottie? Check use of ' and " for dialogue.
Kate called over her shoulder to her husband as she leaned into the back seat of their black Qashqai; usually sleek and shiny but now speckled with mud after their long drive through winding country roads.
Not too fussed about what kind of car it is, still hung up on who Lottie is. Kate was standing on the driveway in front of the house a minute ago and is now leaning into the back of the car, seems a little disjointed, could something tie the two together, her thoughts or what she saw as she turned back to the car?
Kate wasn’t doing much better; she was hungry and grumpiness had set in thirty miles back after the sat nav had sent them in the wrong direction three times. Two phones, two separate sets of Google maps and one mention of a divorce later, they had arrived.
They'd been here before though, seems a little odd that they'd bought a house after seeing it once and not knowing remotely where it was.