Your payslip is extremely optimistic. You can definitely expect between 2100 and a maximum of 2500 net. Because your wife's job on a 400€ basis is not secure, it can also be lost. And you shouldn't count child benefit in the construction budget either. Child benefit has its reason and should be spent on children. (My very personal opinion) There are costs for school/school trips, clothing, sports, and so on... but I don't need to tell you that, you know yourself.
What you should additionally consider now is that a house incurs higher additional costs than an apartment. I would estimate about 300€ per month. And depending on the residential area, there is always the "risk" as a property owner of being charged by the municipality when the sewer is redone or the street needs to be renovated. That can cost a lot of money, and I no longer see the potential for you to build reserves to cover such costs. I think you should always keep such things in mind in advance.
I don't want to discourage you from the project, just encourage you to think about it carefully again.
When it comes to interior work, you also have to remember that materials and tools take a lot of time, and possibly the time you need to do it yourself (meaning you each have to pay 700€ rent during that time).