I know a bit about childhood nutrition.
The bad news is that babies born to mothers with high BMI are more likely to have excess weight, and the weight gain infants have as tiny tots (up to the age of 2 or so) plays a key role in how heavy they will be later on.
So it's basically not a level playing field for your daughter, she will be more likely to put on weight than other kids. I say that as a mother who also has high BMI, btw. That ship has sailed.
On the other hand, the good news is that means your actions now are not really the thing that will determine your child's being above a certain BMI or not. Take that pressure off. The thing that is reliant on you now is teaching her to have a happy relationship with healthy food that nurtures her and gives her what she needs. The right fibre, vitamins, minerals, protein, energy.
Not thinking of food as an enemy, thinking of it as a wonderful thing that keeps her healthy. You could get some children's books on the digestive system, wall charts about different vitamins etc. Instead of seeing eating as something that's tipping the balance, you can think 'these green beans have iron and calcium that does xyz for our bodies' etc.
Good food in the right portions and don't necessarily use her BMI as a sign that you're failing or she's unhealthy. If she's larger in later life, she'll be like you. Is being like you really that bad? You need to think that through.
We've come great strides in a relatively short time around obesity treatments and I'm really hopeful that in future, we'll find better ways to treat and prevent it.
I'd sit down with your family and say you have struggled with weight and food, you want to avoid the same problems for her, and they must take it seriously that you don't want her to overeat or see junk food as a treat.