Floor plan of a two-story house with a slight slope

Terrace, which of course should also be on the south side.

That seems to dominate your thinking a lot. But why? Especially with such a property, it makes sense to position the house and garage as far forward as possible and place the garden behind the house. By the end of the workday, the sun is no longer in the south but in the west. A north-facing terrace is also quite pleasant on hot summer weekends. And no one is stopping you from placing a nice sun bench at the northern end.

What is the view like to the north?

Are there any pictures of the surroundings?

The plot (red arrow) is located on the outskirts of the village.

The canal for the expansion of the building area exists up to the green arrow; many plots north of Grasweg belong to the municipality, but when an expansion will take place is unclear, as is how the houses there will be positioned.

Traffic on the small road on the south side is extremely low, as those who live there all drive "south."

I have also looked at aerial images from other new development areas; I would say 60% have the garden to the south, 25% to the west, and the rest somewhere else or no garden at all.

If I build the house and garage all the way to the south, I would be outside the building line and block my two neighbors’ views to the east and west, which is also unfair, if it is even possible.

If I move a few meters forward, the space becomes narrower again and I have two gardens, and the western part is shaded by the garage of the neighbor on the west side.

You are also welcome to make suggestions or sketches on how to place a house with an adjacent garage there.

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Thank you very much

Regards, Ralf

You are also welcome to make suggestions or sketches on how to place a house with an adjoining garage there.

In the third image of this post, you can see the building envelope.
I would follow the slanted boundary a bit more, especially for a house intended for rental. But in principle, I stick to my semi-detached house proposal.

A semi-detached house does not have everything on one level, at least the semi-detached houses I know are two single-family houses joined together, this option to have everything on one level is a "must have" otherwise I cannot consider it for old age.

In combination with a double garage, one semi-detached house would have to face south and the other north, or what do you mean?

Best regards Ralf

So, let's assume a two-family house…

In combination with a double garage

… then choosing a shared double garage is already the worse choice.

Since I can’t really expand in width anymore, I would have to make the house bigger to the south in order to have another children's room, but then the rooms are long and narrow.

You are thinking too much in terms of "lining up rooms"

so that I have the garden in the south

The garden is wherever a garden is laid out.

The living room is also on the southwest side, where you can expect sun and daylight during leisure time.

Therefore, the patio does not have to be there.

But if I put the front door in the middle in front of the house, then the visitor who rings the doorbell is already standing on my terrace, which of course should also be in the south.

That’s what planning is for, e.g. garage or carport as a room divider, hedge as a privacy screen, or a building structure that isn’t just a plain rectangle.

Building line

That is probably the building boundary? Where is the garage or the parking spaces allowed to be? What does the development plan say about that?

that is also unfair, if it’s even possible at all.

That’s what development plans are for. That is (usually) regulated fairly.

and I have two gardens,

see above. A garden is where the garden is laid out. It can be anywhere, which is usually desired. One place where you could spend the summer days, then possibly a play area. And you said that the ground floor might be for later. Your argument with your wife and the children counts less there.

You are also welcome to make suggestions or sketches on how to place a house with an adjacent garage there.

How, if everything for you is about now and here and in an and-mode?! There are nice apartments with two balconies, facing the street and to the back. In principle: the kitchen on the ground floor is an absolute misplanning and a disruptive factor for the floor plan. So don’t insist too much on your current planning.