Convincing property owners to sell

I would also find out a little about the lady, you can derive points of contact from that. So google the lady's name. She might be pictured in the local cheese rag (online), with her second place in the bridge tournament or something like that.

Do I understand correctly that the "half of the plot" is not yet an independent plot and still needs to be officially separated?

yes, just checked again with the city. A new building would be no problem.

And what exactly did you ask the building authority? The answer "a new building would be no problem" reads more like 'the demolition and new construction' would be no problem. If you ask whether building is allowed there at all, the answer 'house construction would be permitted' would make more sense. Not a NEW building. Or if it is about the 'plot with garage,' then I would think from the answer that 'the new construction of a garage' would be no problem.

With official statements there is no interpretation, only exactly what is said applies. Therefore I ask you again explicitly what you inquired about and what kind of answer you received.

The elderly lady said that she doesn't really know, she has nothing to do with it. Only effort, they still need a new garage... I already said that she shouldn't worry about that...

When I read this, I wonder whether the division of the plot or the demolition of the garage is more expensive than the plot itself. Even an elderly lady should know or suspect that a plot has a good intrinsic value and that selling it could provide her with a more comfortable retirement.

What is the plot worth? And even more importantly: what have you offered her? Or did you just say "she shouldn’t worry about it"?

I'll be very direct and honest now: if someone tells me something like that in matters of business, then that person wants something from me, and my best, and for free.

And what did you ask the building authority? The answer "a new building would be no problem" reads more like 'demolition and new building' would be no problem. If you ask whether building is allowed there, the answer "house construction would be permitted" would make more sense. Or, if it's about the 'property with garage,' then I would think the answer means that 'building a new garage' would be no problem.

Well, there are plenty of people in the countryside who used to buy 2 plots to have a larger garden. And there you can build in anytime without problems; we know many personal examples here. But yes, otherwise the property value and what you offered would be interesting. At 50k, I would never give up any part of my garden if my financial situation was good.

So far, we have offered nothing. The main question is whether she would build on it at all. And of course, it shouldn't be for free. She shouldn't have to worry about the garage because she will definitely be provided with a new one. Also, the area is not used as a garden. There is only the garage and a few bushes on it.

Even an old lady should know or suspect that a property has a good intrinsic value and that selling it could provide her with a more comfortable retirement.

The sales proceeds will likely benefit the children anyway, to whom the property has already been transferred, and the old lady will be concerned about the "right of residence" for her car. For widows aged 80+, it is often only important that the waiting period for the undertaker passes quietly. The car, no matter how slowly one trundles along with it, is essential. Being free to decide when to go water the beloved late husband’s grave and then to Aldi, that's what "still matters" :)

Do I understand correctly that the "half of the plot" is not yet an independent plot and still has to be officially separated?

And what did you ask the building authority?

Therefore, I explicitly ask you again what you inquired about and what kind of answer you received.

What is the plot worth?

So many questions that you have not answered.

Well, there are plenty of people in the countryside who bought 2 parcels earlier to have a bigger garden. And you can always build on them without any problems, we know many personal examples here.

Certainly. But we here don’t know the situation regarding the desired plot. And apparently the OP does not know either.

So far, we have not made an offer.

Why not? Money rules the world. No one feels like wasting time with pipe dreams. Sometimes you have to speak clearly in order to even make the effort to deal with changes.

At first, it’s just about the general question whether it would be possible.

It’s always about the price.
And precisely with these remarks:

I already said that she doesn’t have to worry about that...

And of course, it should not be for free.

… one does not deal with whoever is behind the garden fence. That is no basis. That would be the case if the owner wanted to drive the sale himself but he has this easement or the ballast of the garage on it, so he doesn’t know how best to proceed.
So be careful with such offhand phrases – that can have exactly the opposite effect.

Actually, it probably already belongs to the daughters, but they said that mom, who still lives in the house (she is in her mid-80s), should decide.

Actually? Have you spoken with them?
The interlocutors here (as harsh as it may sound) are the daughters. Plural? Then it’s a kind of community of heirs. Usually quite hopeless: one wants to sell, the other does not. The right to persuade the mom/80-year-old belongs to the daughters.
All I see is a written offer at market or fair value to the community of heirs. The garage is not your problem. Either they want or need money and can do without the plot, or not. If the former, then they will also find a solution for giving up the garage.

Check in advance with the authority and development plan whether a single-family house of an appropriate size is allowed to be built on it at all, not everything that apparently looks possible is allowed. And then check the market value. Preferably, even before the building authority.