The other day, I visited a Luis Vuitton store and said goodbye to a sales associate, who was leaving the store and returning to her hometown.

You 'return to' a place.

Since I had previously purchased some items from the store uander her she had serviced me, she contacted me to inform me of her resignation.

If someone in a store helps/sells you something they are 'serving' you. There is an old British sitcom set in a Department Store called 'Are You Being Served?'.

Her parents and two older sisters are looking forward to welcoming her family.

The original sentence is correct but you don't normally differentiate between older and younger sisters in English.

I was impressed by ther words saying fact that her husband loves her family in Miyazaki very much.

I do not know much about him, but heit is a rare person who decideds to live with his wife’s family.

I wonder what he does for a living, but. As she said he loves the sky and the sea in Miyazaki.,

"I wonder what he does for a living." is a sentence on its own. I would suggest linking the remaining part of your sentence with the next one.

Mmaybe he is a poet or a painter.

Joined to previous sentence to make one sentence.

Since I had previously purchased some items from the store under her service, she contacted me to inform me of her resignation.

This is not grammatically incorrect, but this would sound better "Since I had previously purchased some items from her at that store, she...."

According to her,She told me that she and her family, including her husband and two-year-old baby boy, willould be moveing to Miyazaki in July, where her parents live.

"According to" has a slight negative connotion, leading the reader to think that you don't necessarily believe what the person told you. Since that is not the case here, I made a different proposal.
"Would be moving to" sounds more natural

I wondered what he does for a living, but she said he loves the sky and the sea in Miyazaki.

There are two very different concepts in the same sentence, so it would make more sense to split them into two.

The other day, I visited a Louis Vuitton store and said goodbye to a sales associate, who was leaving the store and returning to her hometown.

"Louis Vuitton" is the correct spelling of the luxury brand's name.
When referring to returning to a place, we use the preposition "to"

Since I had previously purchased some items from the store under her serviwith her assistance, she contacted me to inform me of her resignation.

More natural expressions would be “with her assistance” or “with her help” when talking about someone providing service or help.

According to her, her family, including her husband and two-year-old baby boyson, will move to Miyazaki in July, where her parents live.

The term "baby boy" sounds a bit informal and repetitive, especially since "two-year-old" is already specifying the child’s age.

I was impressed by her words saying that her husband loves her family in Miyazaki very much.

It’s more natural to say "her saying" when you’re referring to something someone has mentioned or expressed.

It’s hard for her to balance work and child-rearing, so the decision is a win-win for everyone.

"child-rearing" with a hyphen is the more common and proper form in formal writing.
Add the article “a” before a phrase like “win-win” to make it grammatically correct. So, it should read “a win-win for everyone” rather than just “win-win for everyone.”