Short Story - Family Moving to the Moon

This sounds like "The Strawberry Window" by Ray Bradbury. As K-H-W commented, there are a couple of slight discrepancies: the family is living on Mars, not the moon, and the money is their life's savings instead of being specifically intended for a return trip.

The wife is unhappy living on Mars and misses their home back on Earth:

"Bob..." Her voice was not bitter, but soft, featureless, and as uncolored as the moonlight that showed what she was doing. "So many nights for six months I've talked this way; I'm ashamed. You work hard building houses in town. A man who works so hard shouldn't have to listen to a wife gone sad on him. But there's nothing to do but talk it out. It's the little things I miss most of all. I don't know — silly things. Our front-porch swing. The wicker rocking chair, summer nights. Looking at the people walk or ride by those evenings, back in Ohio. Our black upright piano, out of tune. [...] All those crazy, silly things... they're not important. But it seems those are things that come to mind around three in the morning. I'm sorry."

The conversation prompts her husband to admit that he's spent the family's savings:

"I threw it away, Carrie, I swear, I threw it away on nothing. It was going to be a surprise. But now, tonight, there you are, and there are those blasted suitcases on the floor and..."

"Bob," she said, turning around. "You mean we've gone through all this, on Mars, putting away extra money every week, only to have you burn it up in a few hours?"

"I don't know," he said. "I'm a crazy fool. Look, it's not long till morning. We'll get up early. I'll take you down to see what I've done. I don't want to tell you, I want you to see. And if it's no go then, well, there's always those suitcases and the rocket to Earth four times a month." [...]

"The freight rocket came in this morning," he said, quietly. "Our delivery's on it. Let's go and pick it up."

He reveals that the "delivery" contains the family's belongings and bits and pieces of their house back on Earth. And when he gets to the final crate:

He ran down the steps to the last and as-yet unopened canvas-covered crate. With his pocket knife he cut a hole in the canvas. "Guess!" he said.

"My kitchen stove? My sewing machine?"

"Not in a million years." He smiled very gently. "Sing me a song," he said. [...]

He ripped the canvas wider and shoved his hand into the crate and touched around for a quiet moment, and started to sing the words himself until he moved his hand a last time and then a single clear piano chord sprang out on the morning air.