First and foremost, though mentioned with the best of intentions, V8 fusion and other types are LOADED with sugars with the exception of regular V8 100% vegetable juice (has 8 grams of sugar per 8 ounces). In a serving of V8 Fusion there are 25 grams of sugar per 8 ounces. For 12 ounces of Dr. Pepper (the one in my hand) there are 40 grams of sugar. This means for 12 ounces of V8 Fusion, there are 37.5 grams of sugar. The reality is substitution is not always a good idea. The only difference between handing her a Pepsi and a V8 Fusion is that V8 actually has some nutritional content.
Give her a vitamin and let it go. My son, who is 5, has been boycotting veggies for what seems like an eternity, along with proteins from meat and anything that is starch but doesn't resemble a french fry or stack of mashed potatoes. I do the same thing at every meal; he has to at least try a food he thinks he may not like.
Sometimes he will continue to eat it without being asked, sometimes he pouts and gets mad. The one bite rule never goes away though, and he gets a Flinstone vitamin every day to make up for he lacks through actual food. And he knows if he doesn't eat enough food, he can't have dessert or any other snack he can think of.
It's really not worth fighting over. And think of it from a realistic perspective, and ask your husband the same question; do YOU like all veggies and foods? Do you eat lima beans and spinach and okra and hominy and every variety of squash? Water chestnusts? Brussell Sprouts? LoL, I eat a lot of those, but not all of them. Even us grown ups don't like everything there is to eat. Think of eating a food you find disgusting or just bad tasting, and then tell me it's fair to force her to eat something she hates (or even thinks she hates)? You can lead a horse to water...