Translation:You have a new, beautiful home. Congratulations!
Indeed, the current translation is incorrect. And I would even say the comma in your translation is optional as well. The two adjectives are not from the same "category" - one indicating age and another appearance - and so the comma can be (should be) omitted.
You have a beautiful new home.
I would go so far as to prefer that word order in the Finnish sentence as well. While saying "teillä on uusi kaunis koti" is certainly fine, I'd probably say "teillä on kaunis uusi koti" since it is the new home (uusi koti) that's beautiful. But of course if they've had a beautiful home (kaunis koti) before, and this new one is also beautiful, then of course you can say that they have a "uusi kaunis koti".
In English, there is a defined order for adjectives (Quantity or number, Quality or opinion, Size, Age, Shape, Color, Proper adjective (often nationality, other place of origin, or material), Purpose or qualifier... Does Finnish have a similar order codified in the grammar?
You can have an old blue Latvian dinner plate, but only a pyschopath has salad Russian small new three forks...