Unfortunately, if your oldest DC has got to 10 and still doesn't eat any fruit/veg, it is going to take you a while to change that.
So it's probably going to be easier to expect her to eat fruit instead of veg, while you gradually introduce more veg into her diet.
Constant snacking means that they're not getting enough food to keep them satisfied - which sounds about right if you're allowing lots of biscuits. I know you don't like people saying this, but frankly they're right - just stop buying the biscuit/crackers/crisps (or whatever they're snacking on).
To break the snacking habit, you need to make sure they're not so hungry between meals. So you should start with breakfast. Stop giving them any carb-heavy stuff, like cereals/porridge, and substitute those with protein and fat-based meals, so stuff like scrambled/poached/boiled eggs. Wholemeal toast will be fine, but make sure it's with eggs, or some other protein. Make sure that they're having full fat options - full fat Greek yoghurt with fruit for breakfast would be a perfect option. Give them full fat milk to drink, and make any sauces with cheese and full fat milk and/or cream.
Don't know what you do about lunches - do they have school meals or are you doing a packed lunch? If the latter, try and avoid the obvious sandwich + crisps + biscuit.
Evening meals are, actually, the easiest. Don't try and make meals like spag bol, where it's obvious there's no spaghetti - but cook something that's meat/fish with veg/salad. They can have potatoes with theirs (children can cope with more carbs than adults, as they're still growing/need the energy), but encourage them to eat more veg with theirs.
If you haven't been giving them veg or salad so far, and it sounds like you haven't, then you may have a bit of a battle on your hands - so start with easier veg/salads; carrots, tomatoes, peppers are generally preferred to things such as broccoli and sprouts!
Things like shepherd's pie generally go down well - you can make the mash with celeriac and leek, or cauliflower. With a good handful of cheese on the top I doubt anyone would notice it's not potato mash.