I can already sense the lack of ability among high earners to imagine a less comfortable life. ;) Of course, it's less convenient without a car. But please don't forget that we are talking about Weidenthal here (I can say that openly since the OP shared the listing with us). This is not a village with 400 inhabitants. The train station is directly on the line between Kaiserslautern and Mannheim/Ludwigshafen. I used to commute there as a vocational student, so I still remember the stop. There is at least a train every half hour to hour per direction, I would say. You can manage with that, as long as the train isn't striking. But they usually strike long-distance trains, rarely S-Bahn trains.
That's it. Of course, that means less comfort, but living with 5 people in not even 80m2...
Living in the countryside without a car is naturally not like in the city. You do suffer some comfort losses. You have to know that. If you are rather home-loving and don't have appointments outside all the time, it might be irrelevant on an individual basis. The OP is already aware of this, at least that's my feeling.
However, I do see the risk that the OP massively underestimates the renovation and restoration effort and the associated costs, and that the house becomes a bottomless pit. So far, I have not gotten the impression that the family is experienced enough here. The financial means to outsource this are unfortunately not available. It should also be clear that pipes and electricity should last another 10-15 years. Otherwise, you live in a dusty shell, which is even worse than living with 3 children on 80m2. More than a few cosmetic repairs or things on the facade are not possible for the next few years for this reason alone, since you want to actually live in there.
Therefore, a meticulous inventory is essential. Only if you truly understand what is ahead should you dare to buy. And no, you do not acquire a basic understanding of electricity, water pipes, heating, etc. in 1-2 days. Usually, you develop that only through (negative) experiences. It is bad if the financial means are missing for that.
Basically, the OP’s model must be as follows: Move into the house in its current condition (minimal effort) and rock the house down for 10-15 years (until the last children have left) and only then carry out major repairs. Legal regulations (insulation, heating) may have to be implemented already when moving in (there is no alternative) and maximum funding should be claimed for that. Since the family's income is rather low, the chances for this are quite good. In any case, the family must go through everything with the bare-bones version – there's no alternative. The family can also handle higher heating costs in winter with their savings rate, so better invest less (keep fixed costs as low as possible) and then just wear one more sweater if necessary...
Regarding the price, however, I am still not sure whether it is not rather too high. If the water pipes and electricity are already 60-70 years old, better leave it alone. The seller will probably not provide information about this – possibly for a good reason.