Is it obligatory to obey a mother who forbids her son from supplicating with prayers from a book of well-known supplications, under the pretext of supplicating with what is in one's heart?

It is permissible to supplicate from a book containing ma'thur (transmitted) supplications if you do not memorize them. This is a good thing, as it contains great blessings and benefits. However, it is better to memorize these supplications so that you can supplicate with them by heart, for this is more conducive to a focused heart and helps in recalling the meanings of the supplication, as Ibn Baz (may Allah have mercy on him) said. You are not obligated to obey your mother in abandoning supplication from this book, because there is no harm to her in it, nor is there any benefit to her in your abandoning it. Therefore, you should strive to please her and memorize what is easy for you from the supplications. If you need to supplicate from the book, then explain to her the virtue of the ma'thur supplications and the permissibility of doing so.