Is it obligatory to inform the wife about her husband's fluctuating cessation from prayer, despite his acknowledgment of its obligation? And does this affect the validity of the marriage?

What is obligatory upon you is to repent from your negligence in prayer. For even though its perpetrator does not become an unbeliever if he abandons it out of laziness, according to the majority of scholars, negligence in it is a grave matter. Severe warnings regarding it have been mentioned in the Qur'an and Sunnah, such as His (Allah's) saying: "Then, there succeeded them a generation who neglected prayers and pursued desires; so, they are going to face (the consequences of their) error" and His saying: "So woe to those who pray, those who are unmindful of their prayer." And whoever does not guard his prayer will have no light, no proof, and no salvation on the Day of Resurrection, and will be resurrected with Qarun, Pharaoh, Haman, and Ubayy ibn Khalaf.

As for the marriage, the marital bond between you remains. You are not obliged to inform your wife about your negligence in prayer. Rather, what is obligatory upon you is to repent, guard your prayers, and conceal your own shortcomings.