I also agree with pps that aggressive intervention with childhood obesity can have long lasting, negative impacts on their health and wellbeing. If you read Isabel Foxen-Duke's experience of this, it gives you some insight. She was put on a diet at the age of three and back and forth to the doctors, because she was a heavy child, just built that way. She ended up with all sorts of mental health problems and drug addiction.
In the 20th century, kids were given amphetamines as diet pills which clearly affected their health. I believe Mama Cass was one of these children and obviously she died young.
I am sure the op is not suggesting any of these methods, but just want to point out that sometimes what some people think is a 'proactive' approach to this can actually be overly aggressive and damaging. If the op is grandparent, she may have raised children or been a child at a time when these approaches were more accepted and being fat was to be avoided and derided at all costs.
She still hasn't said if she made these comments in front of the GD, so I'm assuming she did? If so, it may not be that the mum doesn't think the weight needs to be tackled, but that she doesn't think the OP's approach is the best way to do it. Which I can understand.
It isn't get her slim at all costs. It is such a complicated issue. If you take the wrong approach it can get her slim in the short term but may completely ruin her relationship with food and her body, which could be catastrophic in the long run. Many of the 600 lb people you see on tv have been strong armed into diets as children. Yes, it works in that it gets them to be slim for a short time, but obviously not in the long run. At the other end, eating disorders where children undereat or purge are lethal and absolutely awful illnesses which can sometimes not be recovered from.
So again, don't just have the goal of getting the weight off. There is so much more to it than that.