No worries 
You can normally go on vacation and play your save file with the family you go with or also take other friends from your current city with you. While on vacation you cannot switch households back to the main city. You play the family with which you are on vacation. Your Zois age while you are on vacation if you have aging on. You can buy stuff and bring back home in your inventory and relationships with the Zois you brought with you can be progressed during vacation as well as skills etc.
Before you go on vacation you have to decide how long you want to stay. Maximum is 7 days. Then the game simply brings you back to your main city.
When you come back you are back in your main save file / city and everything is exactly as it was before, just some days have passed.
But be aware of 2 current bugs with this:
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your Zois funds do not change. When you come back you have exactly the same amount as before: Zois funds are deducted to previous amount after returning from vacation - all money earned during vacation is gone
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If you finish your collection log during vacation the items you found there seem to not be recognized correctly once you are back and you have to find these again when back to finalize your collection: Collection log items disappear after trip