Are you truly recovered from your ED op? Because I’m wondering if your eating at some stage turned to restricting to get to a size 6/8. There’s recovered, where you’re in a healthy weight range, but still have disordered thoughts and behaviours. This is not true complete recovery. And there’s truly recovered, where all ED thoughts and behaviours are gone.
As for your dh, his eating sounds disordered and he, and to a greater or lesser extent you as well, are passing that onto her. Asking your dd if she is sure she wants something is anxiety inducing, especially whilst your dh gives her whatever he wants to give her and she wants to eat more so, and confusing. This is all setting her up for ED.
Then maybe think about genetics. Some people have a tendency to hold more weight pre puberty. Dh and I definitely did and slimmed down in our teens. So there could be an element of this going on with your dd. I’m just saying this, because you’re perhaps panicking. And look at the year 6 girls. They growth spurt massively from the start to the end of the year, and it’s normal to carry a bit of extra weight before that happens. Your dd may just end up doing that a bit earlier if she’s started puberty already.
If you want your dd to eat in a balanced way, it would also be good if your dh could do that as well. It sounds as if he has no idea of portion control. And I can imagine you are going to need some specialist advice on diet from a dietician specialising in ED. Do you have the funds to get some help privately?
The way to go is to reduce simple carbs, increase protein and fruit / veg. Aim for complex carbs. The idea being that your dd grows upwards and hits a healthy weight range in the process. Eating protein keeps you satiated for longer and reduces the urge to reach for the biscuits and sweets. So next time your dd comes to you asking for a snack, you could also offer a little piece of cheese (eg a babybel) with that fruit, because it will slow absorption and keep your dd’s blood sugars stable reducing the sugar spikes.
As @ChunkyMonkey36 said, she deals with the food issue before it hits the plate. I think that’s the way to go at age 9. You can make muffins / cakes with 50% less sugar and increase the egg content. Use wholemeal flour. No icing. It’s all about thinking about ways to give your dd a bit of what she wants in a healthy way. And please don’t give her low / reduced fat. That won’t help. Fat doesn’t make you fat.
I would also be trying to get your dd to eat meat again as a priority. Make her favourite meals regularly and eat them in front of her. After 2/3 times of making the same food, offer her a bit from your plate to try, stuff like that. This is because it is not easy to get all of your protein needs from a plant based diet. She should be taking an b12 supplement at the very least. So your dd needs to be eating far more protein than if she were eating meat. Idk what protein she is eating, but that’s a lot of beans and pulses as well as eggs and cheese. Can you talk to her about that? Increasing her protein intake. If she’s fussy, she will likely be horrified.
Age 9, you can’t force her to eat meat, but you can tell her she needs more protein and explain why. Ie it gives you energy. And she needs it to grow into a big girl etc. That may be enough to get her eating meat again.
My dd was always difficult with food, textures etc and to get her to eat vegetables, I told her they made her hair shiny. Maybe you can do the same sort of thing with some foods as well. And I’d be talking about those girls, saying maybe they don’t realise that our bodies need protein and meat is the best one for that. Bla bla bla.