How should a newly committed religious man deal with his wife who refuses to remove the television from the house, does not observe prayer, and he wishes to raise his children according to the Sunnah of Allah and His Messenger?

Your journey on the path of righteousness is correct, and you must utilize the means that aid in steadfastness. Be gentle with others when inviting them to the truth, and focus on teaching and good guidance to strengthen faith. Be a role model for them through affection, compassion, and good treatment. The wife's negligence in prayer is a grave evil, so advise her with wisdom and warn her of Allah's punishment. If she persists and advice does not benefit her, then divorcing her is recommended, unless you see that bearing patiently with her is for the benefit of the children, while continuing to try and reform her.