I wonder why the car was moved from/to Gent so many times

This is easy to explain.
In the summer time (July and August), trams run less frequently in cities: it is holiday season for everyone and schools are closed. In most of the cities, there is then a surplus of trams.
On the coast, it's the opposite: people spend their holidays there, and the frequency increases significantly during the summer months. These are by far the busiest months of the year.

This is therefore a matter of efficient use of trams. Incidentally, the trams on the coast are wider than the trams in Antwerp and Ghent.
As a result, trams from the coast cannot run in Antwerp or Ghent, but the opposite is possible. To this purpose, a number of trams from both cities were modified with extendable steps to avoid a gap between the platform and the tram. This also explains why these are always the same trams that are transferred.