Never try to make a beginner play a piece perfectly or as close to an A grade as possible. It is just useless and frustrates the poor student. A single piece generally should not be under the lesson microscope for more than 1 month, the student is of course required to practice the piece as long as they can, but not all of my beginner students practice ALL the pieces we go through. At the end of the year most of them get through over 20 pieces, they will continue to play the ones they really like and discard the ones which they don't. Some people think it is a waste when you forget about pieces you learnt before but it absolutely is not. You can prove this to yourself by simply trying to relearn the piece, you will get it under you hands many times faster than your previous first attempt (In fact I use this constantly as a motivation point to many of my students when we relearn a piece, because we keep a journal we know how long it took them when they first learnt the piece, ALWAYS when we relearn the piece the amount of time required to bring it back is MUCH shorter than when we first learnt it, students delight in this knowledge.) The brain does not forget paths that we walked before, but the path might get a little thick with "weeds' what have you but the general way is still there and things will start to feel familiar again as you remember things.
You should also be able to play a piece in many different ways and not get stuck playing it in one fashion. Beginners inability to change how they express their music demonstrate 1) lack of technical capability 2) underdeveloped muscular memory which is a slave to the initial prescribed note memory process. As teachers we should set up our students to act against these issues or it will restrict their ability to teach themselves and overall progress further in piano. Even advanced pianists must change their perspectives on things now and then, if we are stuck in a stubborn singular method our progress will plateau.
A beginner of course will get frustrated to have to change a way in which they play a piece after struggling to play it one way. Your idea to try to make her play the LH legato then detached was a good one but you should have told her at the start that there are two ways in expressing it and we will explore both. It is teaching 2 musical voices with one piece, the student does not have to learn new notes and can appreciate the contrasting sounds in the same piece, efficient.
But how you have gone about this process with this student is a little wrong imo. Struggling for 2 months, then trying to change something again, it is like saying, ok you have run around this track 20 times, well done, now lets do the same track again but now you have to hop around. It is a mental torture, do something new! Young students like to do new things, constantly do new things, small manageable pieces. Even if you think it is too easy for them, give them these pieces that they can get through fast and see quick progress. It will give them energy and encouragement to try more difficult things. I do this all the time with my young students, make them do things which is easy to succeed with then we try something more challenging where they trip over but get up and try again and again. Once they are exhausted they can go back to the stuff which they do so easily, it is a good source of self motivation and crucial to young minds.