You could try these:
1. if/when she won't eat her given meal put it to one side and later when she says she is hungry and wants a snack off her that meal back again (I know my DS is much younger but I serve his food onto one plate and he eats off another. I put a small amount on his eating plate but he can see that there is more if he wants it. This way the entire plate of food isn't 'messed' up and the remainder can be safely saved as it has no saliva on it to form bacteria). You might have to expect that she doesn't eat much for a few days though. I think at 3+ it is more acceptable to let her go a bit hungry until she decides to take her offered meals. I also plan our meals so that there is definitely something DS recognizes and likes which isn't making him a different meal but planning our meals to allow for his tastes as well as mine.
2. Reduce snack sizes. So if she gets a snack of an apple to get her through to lunch time I'd reduce to half or quarter of an apple and then tell her when lunch is and that she will need to wait for it. Obviously you get to decide what a reasonable size snack is depending how long it is to the next meal.
3. When it is convenient to do so give her an option for the whole family meal. So asking should we have x or y today (just 2 options and both of them are acceptable to the rest of the family) and let her pick. Then everyone gets that. This could help her feel more empowered and included in the decision. Or just ask which sides to have with the meal, 'should we have chips or garlic bread with our lasagne?' or 'should we have peas or sweetcorn with our pie?' etc.
Sometimes I remind myself of what I saw in Kenya. Kids, like adults, get to eat when there is food, full stop. If there is plenty of food everyone eats more, when there is less food everyone eats less. Homes don't have a stock pile of food just waiting to be snacked on. The cupboards are literally bare until someone shops for that day, that meal. I ask myself how I would deal with DS's requests for snacks in that situation. I'm not talking about undernourished or starving kids either, reasonably well off families that eat proper meals every day still don't stock pile on snacks or alternative options like we do.
I think there are many things like this where we as parents need to change our own behaviour if we want our children to change theirs. it's how we approach the requests or food rejection. Being sympathetic towards her desires/feelings but firm that the meal is the meal, the snack is smaller and the food cupboards are not there to provide every option but to store food for other meals.
Good luck, I'm not looking forward to the time when DS reaches the fussy eating phase.
