Building on the parents-in-law's property

The question about the [Grundstück] was meant neutrally now, that is whether it makes sense for us to share the costs for the neutral [Grundstück].

If the price difference between demolition (estimated 30k) and owning your own plot with a bit of distance (40k) is really that small, I wouldn't hesitate long and would spend the extra 10k. Proximity to the parents is generally good, but at least a little distance is still a great thing.

The demolition would be paid for by the father-in-law.

As already wrote: If you pay together, you should also both be listed in the land register. But it hardly makes a difference whether you are married or not.

My mother-in-law lives in our house, she is very reserved and has her own entrance, etc.

The advantage is when the little ones are sick, and they often are in kindergarten, she looks after them without much effort.
So you would also have advantages on the shared property.

But when selling the property in case of emergency, it will be difficult with strangers.
And it would always be her garden even if you had split it on paper.

Are the other plots in the new development area? Then there is no need to think long, there are definitely young families and that is worth its weight in gold.

And the 10k to 20k difference that the plot costs more can even be advantageous in financing if the bank rates the project as higher value and offers lower interest rates.

Would there be any structural/terrain-modified/visual/etc separation between the house of the parents-in-law and yours? I have some experience, but in our case, there are 70 meters as the crow flies and a very large workshop/shed in between, and yes, that exactly makes the difference. Otherwise, I would not have wanted to do it. In other words, the same property is not always the same situation, so how would it be for you?

: The 3 meters to the neighbor and to the parents' house must be maintained. However, we have to leave more distance to the parents' house because the father-in-law has a tractor and would need to drive it to the hall, which is located in the garden. Sort of as a driveway.