We had/have this same situation with my great nephew. His mom finally just took the bottle away and told him he was a big boy now. When he got thirsty enough or really wanted what was in the sippy cup, he would drink it.
In regards to fruits and veggies, that is still an uphill battle, because he loves bread. But all the bread was causing bathroom problems. They have taken the bread out of their meals, and she offers it now basically as a dessert. We started peeling and slicing fruit. Since he loves peanut butter, we spread a bit on the apples and pears and he loves them. Pnut butter is good in celery too. We use organic natural pnut butter. Also anything he can "dip"! He will now dip carrots, celery, chicken nuggets and even his grilled cheese sandwich! Dipping gets him eating more veggies. When they are at home, she will peel and chop up tomato real fine and put it inside the grilled cheese sandwich. The tomatoes become real soft and are disguised in the cheese, but it is another way to get veggies into his system. Mac n cheese is another way to add veggies. Of course, we don't use the box mac, we make ours from scratch. Cook the mac, mix it with cream cheese, different cheeses, egg whites and milk. But we add a bit of a twist. Layer the mac, then layer it with finely chopped spinach and then another layer of the mac mixture. Bake as usual. About 15 minutes before removing, chop tomatoes and sprinkle with a bit more cheese. Kids love mac and cheese and this is pretty much a complete meal as you have carbs, veggies and protein. To save time, make a big batch, cook it in your corning ware and when it is cool, cut into squares (serving size) and freeze. It reheats beautifully and makes for a quick dinner for you busy moms! And yes, he loves it! Even the spinach. We call it his "special" mac n cheese. He doesn't want any other kind. Coming from a Montessori background, when you have time, bring your child into the kitchen and turn food into a learning experience. Talk about the veggies, have them help wash them. At this age, you will need to cut them, but if they learn by watching you eat your veggies with them, they will follow. And don't forget the dip! It could be ranch, honey mustard, pnut butter, whatever they like.
Another great vegetable is sweet potatoes. These too, you can bake ahead of time and just reheat. Always rub your potates lightly with olive oil and wrap in foil to bake. The texture is much more palatable for newbies to sweet potatoes. A drop of stevia and you are good to go. You can even add a sprinkle of cinnamon. And yes, to make it more kid friendly, place your serving in a small corning ware bowl with a couple of marshmallows on top. Heat until the marshmallows melt a bit. A few marshmallows won't hurt, but the benefits of the sweet potato will out weigh a couple of mm. Yes, you can bake up a batch of potatoes and freeze them in individual servings too.
Most kids love chicken and rice, slip some veggies into that mix as well. But trying to get them to eat them raw or lightly steamed is still the best. One more thing, don't forget the "spaghetti" squash. Once you put sauce on it, they don't know the difference. Another great source for veggies, and yes it really is close to spaghetti noodles.
Get creative! Think of things she likes and try to put them together with her veggies. And remember, their taste buds are changing. If they are a "texture" eater, get food into the texture they like. How well I know that, because I am a "texture" eater myself. Meat and dairy are the toughest things for me to eat myself. Even in my ripe old age, I eat very little meat, and when I do, it has to be "covered up" to get it down. Also remember, just because they don't like it now, keep introducing and reintroducing veggies, they will grow to love them!
If you have time, another great education tool that might help get her to eat her veggies is to grow them. You just need a few, start her own little garden. Kids love taking care of them and watching them grow. Believe it or not, sometimes their loving care makes them want to eat them!!!!! Hope this helps!!!