Morning,
with that income, a 500,000€ financing at 1% interest is already rather tight, currently, given the interest rate situation, it would also be quite tough.
with the costs, minus the equity, you need 700,000€, if the bank keeps the minimum repayment low here, it’s 3,000€ per month.
I already find 2,500€ as a monthly rate way too high for you. Relaxed would be 2,000€.
the alternative would probably be: you give up [Kind Nr. 3], the wife goes to work right away, and you realize this dream, but whether that makes you permanently happier than a third child? I don’t think so...