I summarized the basic principles of How Tokugawa Shogunate treated Dutch (or any foreigner)-Japanese in Early Modern period before in: What happened to the descendants of Europeans (Portuguese, Spanish, various seamen) in Japan after foreigners were evicted from Japan and kept on one small island?

In short, the Shogunate almost reversed the basic policy in the beginning of the 18th century. Until then in the 17th century, Dutch-Japanese had been treated primarily as the Dutch (thus expelled from Mainland Japan together with their family), as shown in some famous episodes like 'Jagatara (Batavia)- Oharu' and Cornelia van Nijenroode (please refer to the linked post), but after than, they were treated as Japanese and not allowed to leave the country.

Surprisingly enough, however, the most famous such kind of children in Late Edo Period was not Dutch-Japanese, but German-Japanese. Philipp Franz Balthasar von Siebold (1796-1866), German botanist, came to Japan as a doctor of the trading post in Dejima, Nagasaki, 1823, got a child with Taki Kusumoto, a prostitute in Maruyama, Nagasaki. The child, Ine Kusumoto (1827-1903), was raised by the former students of Siebold (He had opened a school to teach Western sciences (Narutaki Private school)).

Ine wished to be the first female doctor (gynecologist) in western style, and got tutored by both Japanese and Dutch doctors (this would be very exceptional at that period). Despite of different difficulties (raped by the tutoring Japanese doctor and having children etc.), she once realized her dream in the first years of Meiji Period (though she was later not permitted to act as gynecologist due to the new doctor license system introduced by new Meiji government). She also met her father Siebold again around 1860 during his second stay in Japan (1859-62), and this was also a very exceptional case, I suppose.

Other Dutch-Japanese children unfortunately generally seemed to have been obscure figures in the primary texts and rarely appear out of a few Japanese research articles.

If you are interested in Dutch-Japanese relationship in Early Modern Period, the National Diet Library of Japan offers a decent introductory site in English as well as in Japanese, though not in Dutch......: https://www.ndl.go.jp/nichiran/e/index.html

References (only with English and other European language summary):

• https://siebold-museum.byseum.de/de/geschichte/die-wuerzburger-siebold/ine-kusumoto
• MIYANAGA, Takashi. 'Brief Notes: Concerning Dutch Grave stones in Japan'. Society and Labor, Hosei Univ., 35-2 (1989): 89-218. (in Japanese, but with long English summary)