Sell the house or keep it alone in case of a theoretical divorce?

I have meanwhile reached the point that a joint sale would be the most sensible way, as we could get the best price there

That is a clearly formulated goal - good that you came to it so quickly.

Does anyone here have experience with what the best approach is now or what arguments I could bring in to still get the maximum value for myself in a payout from her?

I have no personal experience with separation. What I always observe is that mixing financial matters with emotional ones in separations contains explosive potential.

There is a difference between the market value and the selling price. The market value is the value that the property is "objectively" worth. Such a value can be determined by an appraiser. The selling price is the price that is agreed upon in practice. I would inquire how the ratio between the market value and current selling prices is in the region. Now there are three scenarios: 1. The market value is above the selling price level. Then have the market value determined and propose half of that as the purchase price. 2. The market value roughly corresponds to the selling price level. Then as in 1. 3. The market value is below the usual selling price level. Then find that out and add the percentage of the usual difference to the market value and propose half of the price determined this way as the purchase price.

Option 3 gives you the opportunity to prevent making a bad deal based on the appraisal. How you can argue to maximize your share against your ex - I’d better refrain from that.

I might be overlooking something... but if my wife and I were to separate now, 2 years after moving into the house, and she wants to continue living there with the children. What exactly would she owe me then, apart from half of what we have invested there, minus what I take with me, plus the increase in the value of the house? She would just have to pay the installments alone, the bank doesn’t care from whom it collects the payment.

That can hardly be more than the equity initially invested a few years after moving into the house, because prices haven’t increased that much and an appraisal will determine a reasonable value, which certainly won’t reflect the desired sale price.
So equity + installments paid so far divided by 2, move out, done.

But even if one wants to sell the house. The person who pays the desired price, maybe 650,000 EUR instead of 600,000 according to the appraisal. You have to find that person first, which can take months. Do you want to keep living together in the house during that time?
So in that case sell quickly for a reasonable price, repay the loan, and split the rest by 2.

Do you really want to argue for months over a few thousand euros with a net income of 4,900 EUR/month?

I might be overlooking something... but if my wife and I were to separate now, 2 years after moving into the house, and she wants to continue living there with the children. What exactly would she owe me then, apart from half of what we invested, minus what I take with me, plus the increase in the value of the house? She would just have to pay the installments on her own then; the bank doesn't care from whom they collect the payments.

That can hardly be more than the equity invested a few years after moving into the house,

If both remain jointly responsible for a loan, that’s not a good deal. The lending bank has to agree to such a thing.
I have no knowledge regarding the existence or amount of a loan contract. The likelihood that the majority of the house "still belongs to the bank" is quite high.

Usually, the payout fails because neither party can really afford it, and the house ends up being sold after all.

A prerequisite for her to keep the house would very likely also be that you are released from the loan, she handles the payment alone, and can pay you out. I suspect she hasn't had any major salary increases recently, so I would first put a question mark on whether that is even realistic (and if the banks agree to that).

All the best in any case.

There is apparently a new partner; if they participate, that should not be an issue for the rate... all these speculations do not help. He has to get out of there as quickly as possible, even if that does not represent the absolute optimum for the finances. Money is not everything... especially not when you can quickly build something new with 4,900 net.

Thank you for the many responses. I really find the forum helpful because I had not dealt with the topic beforehand, as probably very few have.

Sell as best and as quickly as possible and then start your own life anew on your own, whether she spends the night somewhere else 20 or 38 times. You may still be inflicting unnecessary pain on yourself, that is exactly what I would change myself and not wait for the other person to change it for me. I want to be the captain of my own ship again, a wise friend once told me.

I see it the same way and that is why I would like to take the next steps here now that some calm has settled in, and the staying overnight should only illustrate how we currently live here. As far as she is concerned, she can do whatever she wants, her life and her decisions.

I just realize more and more for myself that I have to actively shape my life again, and just the fact that I no longer feel responsible for her illness (depression) already brings me a lot of joy back that somehow got lost over the past years. But completely independent in my own living space would be even better and that must be the next step.

That is a clearly formulated goal – good that you came to it so quickly.

I would inquire how the ratio of market value to current selling prices is in the region. Now there are three scenarios:
1. The market value is above the selling price level. Then have the market value determined and propose half of that as the purchase price.
2. The market value approximately corresponds to the selling price level. Then as in 1.
3. The market value is below the usual selling price level. Then determine this and apply the usual percentage difference to the market value and propose half of the price determined in this way as the purchase price.

Option 3 gives you the opportunity to prevent making a bad deal because of the appraisal. How you can argue to maximize your share vis-à-vis your ex – I better stay out of that.

Thanks again for the transparent explanation. Sorry for the possibly "stupid" question, but where exactly do I get the difference between the current selling price level and the market value?

I only found one example online, a house from 2015, 2 streets away, gas heating etc., smaller living space (130 sqm versus 180 sqm), but 80 sqm more land than we have here, is being marketed by the local savings bank for €600,000.