This sounds like The Store of the Worlds by Robert Sheckley.
A man has very a ordinary life, with wife and kids and jobs, and passes a new shop making strange promises
Not quite. The family comes up later. The story starts with the protagonist (Mr Wayne) visiting the shop which has been recommended to him. There are hints of a post-apocalyptic world.
Mr Wayne came to the end of the long, shoulder-high mound of grey
rubble, and there was the Store of the Worlds. It was exactly as his
friends had described; a small shack constructed of bits of lumber,
parts of cars, a piece of galvanized iron and a few rows of crumbling
bricks, all daubed over with a watery blue paint.
to take customers to revisit a memory? Or to a different stage of their life?
Or the many-worlds of quantum mechanics...
The shopkeeper, Tompkins, explains.
'What happens is this. You pay me my fee. I give you an injection
which knocks you out. Then, with the aid of certain gadgets which I
have in the back of the store, I liberate your mind.'
'Your mind, liberated from its body, is able to choose from the
countless probability-worlds which the Earth casts off in every second
of its existence.'
'That's why I charge so high a fee; to get materials, to experiment.
I'm trying to find a way of making the transition permanent.'
He is also told that the strain will take ten years off his life expectancy.
And in the end we learn that he's actually bought the package
There is an interlude where Wayne goes about what appears to be an ordinary life, sometimes musing about whether he should take Tompkins up on his offer. Then he comes to in the shop and it is apparent that this interlude was his desired alternate reality.
for what is precious to him - a button and I don't know what else
Wayne is clutching a parcel while talking to Tompkins. After the experience:
Mr Wayne undid his parcel and laid its contents on the table. The
parcel contained a pair of army boots, a knife, two coils of copper
wire, and three small cans of corned beef.
the reality is post-apocalyptic, and his family is gone, and the town is ruined.
With the aid of his wrist geiger he found a deactivated lane through
the rubble. He'd better get back to the shelter before dark, before
the rats came out. If he didn't hurry he'd miss the evening potato
Already mentioned in answers to another question
... with link to google books