I think first you need to find out what is difficult about eating the leftovers.
Is it knowing that the leftovers exist in the first place? Is it too many steps (making the easy snacks a more attractive option in the moment) - pulling the big pot of leftovers out of the fridge, placing into a portioned container, and then warming it vs just opening a bag/box? Is it a dislike of the texture/flavor the next day? Are some leftover dishes eaten more easily than others, and why? They will say "snacks are easier" -- but what about the process of getting a snack is easier and more appealing then getting a leftover meal? The taste? The process of preparation? Are they not hungry for a meal but only want smaller amounts of food, so a full meal is overwhelming? Etc.
Each of these problems would require a different solution. So knowing the underlying reason *why* the leftovers are sitting uneaten would help you actually create a durable solution going forward.
As an example: I'm an extremely lazy person; if I'm looking for a meal and I'm faced with the daunting task of pulling a big pot out of the fridge, grabbing a bowl, scooping out a portion, waiting for my bowl to warm in the microwave, putting the pot back, etc vs just pouring myself a bowl of cereal, the cereal wins every time. I know it's absolutely a ridiculous problem, but it doesn't change the fact that theres difficulty in that moment for me for whatever reason. Also, I'm not the primary cook, and sometimes there's "plans" for the pots of food in the fridge and I'm a little leery of eating something that may have already had something planned for it. So I end up not eating leftovers UNLESS there are pre-portioned containers in the fridge. These containers serve the purpose of clearly delineating that these are for eating, and all I have to do is pull one out, pop in the microwave. No dicking around with lifting heavy pots, no analysis paralysis of deciding how much I want to eat, no finding serving utensils, etc. So the preportioned containers solve my particular leftovers problem, but may not actually solve your family's problem.