Is it permissible for a husband and wife to bathe together before or after intercourse, and how can a Muslim woman protect herself from that which protection is sought from in the bathroom if she is bathing with her husband, knowing that she recites the supplication for entering the lavatory and covers the place of the lavatory?

There is no harm in a wife obeying her husband in what he commands, as long as the Sharia has permitted each of them to look at the other's awrah (private parts). To protect against devils in the bathroom, one must continuously recite the prescribed ذكر (remembrance/supplication) for that, such as saying: "In the name of Allah, O Allah, I seek refuge in You from all evil and evil beings."