I find all of this very solid and definitely doable. It was quite similar for us, and we are also very safety-oriented.
After the elimination of daycare costs (from age 3 it is free in NDS, so only the meal money remains), you have even more left over. Of course, children cost increasingly more, but your wife might be able to work more again in a few years? Or is another child planned? Then I would plan that out once. During my parental leave extension, which I then had to lengthen beyond the parental allowance because no daycare place was available (legal entitlement or not), we had significantly less money, but that was foreseeable and therefore manageable.
Normally, I would also say at least switch her to a cheap small used car that is paid for in cash. But you don’t necessarily have the money for that right now, and since our cash-paid used car just came out of the workshop, I don’t think leasing modern vehicles is such a bad idea at the moment...
For that area up there (I roughly come from that direction) I find the price okay. You are probably too close to OL to find something (still) cheaper. I would do it if the house is right for you.