I am sorry that you had to have health problems, but, as you say, this is an opportunity to make some changes in your life.
First, I would make a "rule" that there has to be a piece of fruit at breakfast (and at other meals as well, but at least at breakfast), and veggies at lunch and dinner. Every day.
A piece of fruit is better than fruit juice, because you are getting fiber along with the fruit, and it limits the amount of fruit sugar and calories that you get. One serving of fruit in the form of fruit juice is about 1/4 to 1/2 cup (60 to 120 ml), which isn't very much. It's so easy to drink a large glass or two of fruit juice because you're thirsty. Fruit is good. Too much sugar is not.
Veggies serve a couple of purposes. One, is for vitamins and minerals. Two, is for filling us up so that we don't have as much room for other calorie-dense foods. It might be fun to explore, with the family's help, what veggies might be tasty to them and how to prepare them. And of course, there are all sorts of ways to disguise them in other foods, such as meat loaf.
If you start with these two things -- real fruits and veggies -- then you've made a great start on getting the minerals (including potassium) and vitamins and fiber into your family's diet.
I have to admit that Im not a great fan of veggies. But I realized that, except for slimy mushrooms, I don't really hate
veggies. I merely find other foods tastier. So, I just make it a "rule" that I have to have veggies at both lunch and dinner, and I eat them first, so that I can then enjoy the parts of the meal that I like better. I have also found ways to put veggies into all sorts of things so that they're not so apparent. I chop mushrroms very fine and cook them in spaghetti and risotto -- that way they add goodness and flavor to the dish without my having to chew on their sliminess. Let your kids be involved in creative ways to hide veggies. And let them give creative names to things -- it's a lot more fun to eat "leprechaun trees" (or whatever) than to eat brocolli.
It sounds like you have the opportunity to explore some new culinary adventures with your family.