Hi @Freetown
I cannot advise about in which country to deliver a child. I will point out, however, that your wife may have issues with the costs of the delivery if she does so in the Netherlands. If she has German health insurance, then this also includes the European Health Insurance Card (EHIC). This, however, is intended only for emergency medical treatment while travelling in the EU and so she may have issues if she tries to use it to cover the cost of a delivery.
A new-born child of foreign parents is only entitled to German citizenship at birth if a parent has been in Germany for at least five years and has permanent residency (Niederlassungsleraubnis). As your wife has a limited permit for 3 years, the child is entitled to a resident permit according to paragraph 33 of the immigration law here in Germany. If your wife at a later point becomes a German citizen, then the child will also receive German citizenship.
Best,
Éanna