How should I deal with my disbelieving mother-in-law who rejects my religious commitment and insists on taking pictures of my son, playing music for him, and going out with him alone, while I avoid her sometimes due to my poor treatment of her?

A Muslim must possess good character and deal kindly even with non-belligerent disbelievers, but without compromising the religion or neglecting duties and obligations. One must also care for their child and raise them with a sound Islamic upbringing. If the non-Muslim grandmother wishes to do something that contradicts proper upbringing, she should not be allowed to do so. Otherwise, there is no harm, provided there is supervision. As for her dislike of the niqab and beard, it is not surprising. One must continue to adhere to righteousness and steadfastness, and not seek her pleasure at the expense of disobeying Allah, while striving to invite her to Islam through endearment. As for your husband, he must honor his mother, treat her kindly, and accompany her with goodness, even if she is a disbeliever or commands him to commit sin or disbelief. He should not obey her in matters that contradict Allah's law, while still being kind to her and not harming her.