Disclaimer: I know nothing about playing, reading, or teaching music. But I have had to use translators in my work.
TL;DR: Train the mother.
It's helpful to avoid asking as many open-ended questions as possible at first. (Open-ended questions are those that require more than a yes/no/single word response.) Asking closed-ended questions requires exact translation and will give you an idea of the mother's ability to translate your English precisely.
If the mother 1. answers for the child, 2. gives you an open-ended answer, or 3. Gives you a longer answer when her daughter's was short, or vs. versa, you know the mother is doing a sub-par job of translating.
If the answers seem to be correct, then this "trains" the mother to translate well.
E.g. Instead of,
This notation is complicated. What do you think he wants you to do?
This notation is complicated. Do you know what he wants you to do?
After she answers, (yes, no), give her options (I'm out of my league here, but, e.g.),
Do you think he wants you to play softly/louder/quickly/staccato/whatever?
These kinds of questions - especially as they get more difficult - make it pretty easy to assess 1. the mother's understanding of musical notation, and 2. how the mother is translating. Knowing this helps you to prepare for a less frustrating experience.
If Mom is doing a bad job, set a boundary. Appeal to the mother's values if you know them. For example,
In order to give her the best lessons possible, I must ask you to please translate my questions and directions exactly as I phrase them, or your daughter will not make good progress. I need to understand what your daughter thinks/feels/understands about the music.
As @English Student's excellent answer states, getting her to learn to speak English, even if you are doing so initially - This is "allegro". (have her repeat.) - it will help.
In the Emergency Room, we would routinely, especially during holidays, get foreigners coming in who spoke no English. There is a medical translation system in place, but it was very frustrating. I remember a Ukrainian couple who brought in their baby, who had a fever. I would ask, "Has she been vomiting?" The translator would ask something short. The mother would launch into a five-minute answer. Then the translator would answer, "No." How frustrating!