Problem #1 is that her father is doing something different than you are. If you are together, then you have to work together. If you are not living together, then you have no options as far as he is concerned, and you can only control what is in your house.
Problem #2 is that you have junk food in your house.
Problem #3 is that kids usually have to try things at least 20 times before they really make it part of their diet. So keep offering it, without drawing battle lines.
Then, work with what you have. As TF says below, make food FUN! And for me, it was about creating healthy versions of the food she likes, even if it means (in the short run) putting it in the box of the processed version and then serving it. So keep the waffle/pancake/nugget boxes and put your own version inside. Here are options:
1) Make chicken nuggets but cutting up chicken tenderloins or boneless breasts, dipping in egg and then a breadcrumb mix (I use some combination of wheat germ, wheat bran or whole wheat panko, whatever I have, often with ground flax seed/meal added and a little salt/pepper), then quick-fry in olive oil or avocado oil (any healthy fat) until brown and crispy. I often just get the outsides brown, then finish in the oven. I put them on a baking rack on a baking sheet so the bottom side doesn't get soggy.
2) oven fries - slice potato wedges (skins on) and toss with a healthy oil, then bake in the oven until crispy/browned. Do it with the nuggets and you're only dirtying one pan. You can progress to sweet potatoes or mix them half/half. Kids also like those little fingerling potatoes or mini white, red and even the blue skinned ones mixed together. The smaller pieces cook faster, obviously - usually 15-20 minutes.
3) Do oven roasted veggies the same way - broccoli, zucchini, even beans and asparagus (which take less time).
4) Mac & cheese with real cheese, whole wheat pasta, and butternut squash.
5) Zucchini "chips" dipped in oil and then a mix of whole wheat panko crumbs and Parmesan cheese. Put on a baking sheet or parchment paper and bake in oven until crisp and brown. You can do a few of these in the toaster oven.
6) Make your own pizza - make a sauce ahead of time with spinach in it, and buy a whole wheat pizza crust or even naan bread, then make a pizza "face" with green pepper eyebrows and slices of turkey meatballs for "eyes" and so on.
7) Get one of the cookbooks for kids about hiding nutrition in foods and making the presentation appealing. There are all kinds of things you can do with butternut squash, cauliflower and spinach in a puree form, then add to things. Homemade spaghetti sauce is one. You make up a bunch of puree, freeze them, and then pop them out as needed to add to what you're cooking.
8) "Power pancakes" - you can make these with all kinds of add-ins, including oatmeal, wheat germ, protein powder, flax seed, and more, then add in some bananas or blueberries. Use a small amount of real maple syrup, honey or agave rather than the junk pancake syrup that is mostly high fructose corn syrup with a dash of maple flavoring. Use real whipped cream and make a smily face on it, or use the whipped cream for "hair" with a couple of bananas for eyes and some strawberries for "earrings" and a curve of real chocolate chips for a mouth. You can make the pancakes ahead of time and freeze between sheets of waxed paper, then add the toppings with your child so she has fun creating her own.
10) Make healthy cookies, granola bars and bananas/zucchini breads. I have a great recipe for bars with almond or cashew butter, oats, dried fruits, a little honey, eggs and flax seeds I posted for someone the other day, PM me if you can't find it.
11) Make fruit kabobs on long toothpicks - a grape, a piece of melon or kiwi, a berry, and so on. Mix it up. Stick them in a half of an orange, inverted on a plate, and call it a porcupine. My son was picky and we made fruit his "first half" and the waffle/pancake his "second half" of breakfast. Sunday was "upside down day" and he at in the opposite order, but he always felt his meal wasn't complete without the other half.
Does this all take more time than opening a box of processed stuff? Yes. But it's worth it.
You cannot make food a battle. You can say "yum" all the time with what YOU are eating, and you can let her down from the table if she doesn't want what's out there. She can have PB&J (upgrade to natural PB and real fruit preserves or All Fruit), but you don't give in to demands. The assumption you make is that she is not hungry or she can have the healthy option. But you don't go to McDonald's because she's unhappy.