Assuming these meals are all vegan, you need to give your kids meat. I know you think it's wrong, meat is murder, etc - that is your thought process, you decide what you eat. Your kids should make the decision for themselves whether they want to be vegan or not. They will hate you if you push it on them.
Your DC probably doesnt want to eat this food because, in the least offensive way possible, it doesnt sound too appetising, especially to a child. The fat and protein provided by meat is what your child's body is craving. Its craving nutrition. You need to feed them meat. Im sorry but I will say it as many times as is necessary.
Im not saying you have to only feed them meat, but introduce it to them. It would most likely stop your refusing to eat predicament.
Would like to add, my son is the same, and he has autism. Takes literally about an hour or two to eat ANY meal, but doesnt refuse to eat it. He just gets distracted. Does your daughter get distracted too, and thats why she takes a long time? Or is she sat at the table, plate in front of her, not wanting to eat the food in front of her?
That dessert / pudding is the only thing she looks forward to, and taking it away as punishment for not liking what food you give her isnt the best way to go about it. I know your at your wits end, ive been there with my son. But perhaps going forward, try new meals (containing meat!), see if she likes them. She may eat it so fast that boom, your problem is gone.
If it doesnt change anything, consider other possible causes. Im not saying she has autism or any other condition, just that it would be highly mindful of you to take that into consideration - especially with the head hitting, verbalisations, etc.
Would like to add that you've highlighted she doesn't have an issue with sugary / carby foods (pasta, fruit, yoghurt, porridge), because they contain sources of actual energy. Vegetables just dont. They are low calorie, they are not nutritious enough to be the main part of a meal.
Im sorry of this sounded bitchy at all, I really didnt intend it to. Just please feed your kids meat, they need it. I wish you the best OP, I know how it is.