New construction planning - where do I start?

A monthly installment of €2000 is feasible for us.

You have €55k gross per year. That makes just over €3,000 per month with tax class 3 and 2 child allowances + €450 mini job.
That means 57% of your income goes toward the loan. Without reserves or anything similar. No bank will go along with that.

No one wants to upset you, but don’t deceive yourself.

our parents are also supporting us.

According to your statement, your parents have a low pension, so that doesn’t add up.

My parents don’t have that much pension - my wife’s parents have a bit more. I’m not saying they give us 500€ a month, but when the car insurance bill comes in at the end of the year, they sometimes say "We’ll pay you the 500€ as a Christmas present" or something like that...

3,050€ net, plus 400€ child benefit (soon probably 600€), plus 450€ mini job. 13.5 monthly salaries as mentioned.

I don’t want to split hairs, but it would be just under 2,000€ installments with just over 4,000€ net income, so about 50%.

Honest advice, go to the bank with your numbers. Lay the facts on the table and see what you get. Between 2012 and 2017 there is the new credit policy, the calculations are different there and there is also no longer a "Nasenfaktor".

My parents don’t have that much pension - my wife’s parents have a bit more. I’m not saying they give us 500€ a month, but when the car insurance bill comes in at the end of the year, they sometimes say "We’ll pay you the 500€ as a Christmas gift" or something like that...

3,050€ net, plus 400€ child benefit (soon probably 600€), plus 450€ mini-job. 13.5 monthly salaries as I said.

Don’t want to split hairs, but it would be just under 2,000€ installments with just over 4,000€ net income, so about 50%.

Might be, but on top of the installment there are still 400-600€ additional costs. No idea how that’s calculated with 2 housing units. I calculate about 400€ additional costs per month on top of the installment.

The additional costs I also have today, since I own and live in a house... My parents also pay the additional costs for [Ihre Wohnung] themselves.

Ok. Then make an appointment at your house bank and ask for 600k€ or 650k€. They will then tell you if it is affordable.