This happened between my mother, my daughter and me. It was such an insidious process that it took me a while to realise what was happening. Unfortunately, by the time we realised, the damage had been done and any attempt to take back control meant that my daughter felt we were entirely in the wrong which, of course, my mother encouraged. We did family therapy to try to get things put right but all the therapists kept saying was that it was normal for grandparents to spoil their grandchildren so we wondered whether we were being unfair. Eventually, it was engineered by my mother for my daughter to leave home in high dudgeon with me being persona non grata. Guess where my daughter chose to live!!
I needed therapy after that and the counsellor was very clear that I had been given bad advice and that under no circumstances should I leave my other children with my mother without me being present so they didn't get "groomed" too. Meanwhile, my daughter who was thoroughly spoiled by this time found that her GM's partner was not such a pushover so she ended up falling out with him and left her GM's with much unpleasantness.
Fast Forward 17 years and my daughter will not allow her daughter to be in my mother's presence without one of us being around. She can see how undermining my mother is and will not make the same mistake.
I don't know what the answer is and I fear that it is too late for the mother of your young person to take back control. I suspect she can only talk to her daughter about good relationships and support in the hope she can make some inroads into the damage the Grandmother is doing.