Well remember Scripture is not the only pillar of revealed truth there is also Sacred Tradition, which are not the traditions of men but the Teachings passed through the Apostles. In a very real way the Church did not come out of the Bible the Bible came out of the Church.
You likely do not want to get into a debate with family on it too deeply but think...where does the authority come from to establish a canon of Scripture. Where does the authority come from to decide whose decision on what books are Scripture and therefore are valid?
This in no way diminishes Scripture, which is an incomparable treasure, but we do need to look at that question.
So without a Church, with authority given by God, what prevents anyone from deciding any book or work should be Scripture and say the Holy Spirit guided them?
So any appeal to Scripture and the, real and powerful, authority of it must take into account how we know the Bible we have is correct. And that answer rests in the nature of the Church.
As far as consulting Scripture on Catholic beliefs this should help you narrow down where to look:
Catholic Faith - Scripture Catholic
So my advice is if your mother, and may God Bless her, is concerned...engage gently. Go to the link and pick some areas that address topics that might concern her. Find some verses to go over with her.
Any mother who encourages her child to read Scripture is a treasure, so engage gently. And the first part of my answer should not be presented to her in any gotcha manner (some would do that, I do not think you would from reading your posts). The first part of my answer (about the Bible coming from the Church) was for you to see the relationship between the Church and Scripture. I would not present that argument to her until some you time after you go over some of the verses from the link. If she begins to see that the Catholic faith is not against Scripture, then you might want to explain how establishing the Canon of Scripture is a duty entrusted to the Church to prevent the personal decisions and biases of men to determine it.