Is purchasing a house and complete renovation affordable?

That would still be a good 4.6k net. To put that into numbers. I leave the assessment up to everyone. Although you can still adjust that almost arbitrarily: child benefit/-allowance, splitting, maybe she only works 50% or maybe 80%, possible salary increases,...

Sounds like a lot at first, but if you subtract the rate of 2300 euros from that, plus car(s), insurance, electricity, water, sewage, garbage, groceries, clothing, gasoline, etc., then in 2023 that is not much anymore.

I get that. Ski vacation in Switzerland is no longer an option. But a good €2000 after cold housing costs is actually quite average when you consider the total population and not just the homeowners. Additional costs will be below average due to the [Kernsanierung], which compensates for part of that.

with the costs you mentioned and the available income, I would also feel uneasy with such a high monthly burden of >2k plus for the loan and the monthly additional costs for electricity, heating, insurance, etc. it might be manageable as DINKS, but it will get tight at the latest during parental leave. on the other hand, the (for you) top location is certainly a great advantage in this phase of life

two variables you can adjust: increase budget or reduce costs
- can anything still be done about the purchase price? your conditions are already very good, but maybe you can talk to relatives again. grandma’s little house carries a lot of emotions, perhaps one or the other relative would prefer to see the likeable nephews/nieces with potential offspring there rather than an investor or newcomers with lots of money
- sell part of the plot to a neighbor?
- take advantage of subsidies. Given the poor energy condition you describe, there should surely be something available (kfw, bafa). what does the energy consultant say about that? I haven’t read anything about this so far
- where can you cut costs in the renovation?

- how about letting the idea of sumbiene circle in your mind for 2 or 3 days?
without children, it might be quite okay to live in the described scenario and it would also be paid off quickly. in the meantime, keep planning and selling is always an exit strategy.

Is the house “uninhabitable” in its current condition?
Otherwise, I suggest you buy it, do some renovation and consider it a temporary solution. As 11ant always nicely writes.... Zwischenhaus ...
You secured the bargain and paid it off quite quickly and then you see what happens next.

With a loan installment of 2,300 EUR, plus additional costs, plus 2 cars... that's still enough for the Baltic Sea or Mallorca.
If you add 2 children, there's no money left for any vacation at all.

We have a similar income, but half the installment. It's enough for a good life, no question. But we're definitely not faced with the choice "Ischgl or St. Tropez?" or "5 Series or E-Class?"

Not for nothing does the bank allow a maximum(!) of 40% of net income for the loan.

With a loan payment of 2,300 EUR, plus additional costs, plus 2 cars... there's still enough left for the Baltic Sea or Mallorca.
If 2 kids are added, there's no money left for any vacation at all.

We have a similar income but half the payment. It’s enough for a good life, no question. But we are definitely not faced with the question "Ischgl or St. Tropez?" or "5 Series or E-Class?"

It's no coincidence that the bank says a maximum(!) of 40% of net income for the loan.

True, it’s simply unthinkable that you might not be able to go on vacation for maybe 10 years. As if going on vacation were a fundamental right.
Everyone has to decide that for themselves.
And you don’t have to be able to offer your child everything, and they will still grow up happy.