Please post an aerial photo of the property area. The address is of course the best help.
Could the house be shifted a bit towards the north?
"The barn may only be moved in the axis during the new construction to the extent that the property areas do not overlap. According to the building authority, a dam thickness of 25 cm is approved as an increase in the cubature."
I'll give it a try, although it is a bit complicated.
Attached is the aerial photo. Everything within the red frame is approximately what will later be our property. The barn itself is number 1 in the picture. Number 2 is the parents' house. The arrows indicate the possible access routes. At the first arrow, there is already a carport which we use. At the right arrow there is a gate; we could also create an access there.
In the photos you can see the barn from the south and west sides as it currently looks.
We are allowed to shift it towards the north; currently the barn stands about 1.40 m away from the parents’ house. It is currently uncertain whether we are allowed a 1x3 m distance or 2x3 m (which would be usual, also/especially for fire protection reasons).
Edit: Roof pitch is about 47 degrees.