Upvote:3
This plan will probably be considered a by passing of Austrian (and most other countries) laws.
In theory, since you are not an Austrian resident you are not required to register the car after 1 month.
But since the car will (I assume) remain by your family, that are residents of Austria, it will be assumed that the car is being used by Austrian residents.
This will be considered a form of tax fraud, since the Austrian road system will be used without paying the taxes that finance that system.
Assume as a general rule: Where the car is predominantly being used, is where it should be registered.
Registration rules
If you have your main residence in Austria, you may use your car or trailer with foreign number plates only for one month in Austria. The one-month period starts when the vehicle is first imported into the country. A temporary removal of the vehicle from Austria does not interrupt this period.A one-month extension is possible if there are convincing arguments as to why you couldn't register your car on time. No further extension is possible.
When the registration periods expires, you have to hand in your registration certificate and foreign number plates to the relevant regional police headquarters or district authority. From then on, you must use Austrian number plates, for which an Austrian car registration is required. If you fail to register your car on time, you will need to pay penalties.
Sources: