There are a couple things I do here to help make sure we eat enough vegies.
First thing I do is, peel (if needed) and cut them up as soon as I get them home that way they are ready to go and only a small amount of preparation is required at meal time. I know a lot of people do this now and it's exteremly helpful.
I've taken it a step further now and I cut up my ham along with any other cold meats, rockmelon, watermelon and also my cheese. I've stopped buying grated cheese after I actually looked at the price and realised it's dearer per kilo and when I found out they put extra things it it to stop it sticking together etc. So I now buy a big 1kg block and grate a third of it and cut the rest into pieces for Rat_girls lunch and stacks.
This doesn't just make it easier at meal times for me, it means that Rat_girl can help herself. She just goes to the fridge and gets some cut fruit or some carrot sticks or some cheese or ham or whatever. Oh and also boiled eggs, I also boil 6 or so eggs every 2-3days and put them still in the shell in a container in the fridge and shell as I need them.
There are some tips to make your vegies last longer, don't wash them before you put them in the containers, water drips off and sits in the bottom, wash them as you use them. Put the containers (this goes for anything) in the fridge with the lid off for a few minutes, let the cool air into the container. And when you open the container if there is condensation on the lid dry it off with a tea towel.
The other thing I do is add as many hidden vegies into my cooking as possible. Yes I still serve vegies on the side because kids need to still learn it's important to eat them. But just incase I throw some more in.
Here is an example of a normal bolonese sauce in our house.
I use this to chop them up nice and small
then throw them in, there is all sorts in there broccoli, caulilower, zucchini, carrots, onion, mushroom, capsicum plus probably some other randoms that I found in the fridge
Then meat and sauce, I use passata or a similar home style brand, it's cheaper than pasta sauces and will last (if you freeze left over in portions) for 2 or 3 sauces.
And there you have a bolonese sauce filled with plenty of hidden vegies....mmmm
