What should a wife do if her husband swore that she would not do a certain permissible thing—namely, that she would not read about pregnancy on the internet—and she has read about pregnancy-related topics several times? What should she do so as not to violate his oath?

It was obligatory upon you to obey your husband in what he commanded you and swore you to, because it is among what is good, and obedience to the husband in what is good is obligatory. In addition, fulfilling an oath is recommended in Islamic law. Since you have done what he swore to abandon, you must inform him so that he may expiate his oath, for the expiation is upon the one who swore the oath.