My kids are just a year younger than these -- 4 and 1 1/2 -- and this is what works for me.
Mac and Cheese
If they like mac and cheese, it's easiest to make in batches, because it reheats quite well.
I chop some bacon coarsely and cook it gently until just browning. You can at that point remove the bacon with a slotted spoon and use the fat for the sauce, or remove it all and use butter; the bacon is optional anyway but very nice. You want roughly 2-4 Tb of fat.
Put 1 1/2 cups of milk in a saucepan and bring to a strong simmer. Add 3 Tb flour to the fat and cook over medium heat, stirring constantly, until very smooth. Continue stirring about 3 minutes or so until the roux has a pleasant, nutty smell, but is not yet turning noticeably brown. Remove the pan from heat. Add the simmering milk all at once and whisk until smooth. Return pan to medium heat and continue stirring and/or whisking until the sauce thickens, which won't take long.
Now stir in a bunch of grated or shredded cheese, gauging quantity by when the sauce consistency is the way you like it. Cheddar is unfortunately not a great choice here, as when reheated it has a tendency to produce little granular curds. Almost anything else will do fine. Be sure to use some Parmesan or the like somewhere in there, but I find that mac and cheese made with only Parmesan is too salty and intense, at least for little kids. Depending on the type of cheese and the way you like it, you will need between 1/2 cup and 1 cup of shredded cheese.
Taste and correct seasoning. If you want to add pepper, I advise you to use only white: little kids sometimes get shirty about little black dots in their food. If these kids are like that, you may want to skip the bacon as well; cubes of ham will do as well, or just skip it. I do not find that nutmeg adds anything significant to the taste that the kids will appreciate, and much more so cayenne.
Off heat, fold into the sauce about a pound of cooked macaroni. I find it difficult to gauge just how much macaroni works with a thick sauce, so add half of it and then stir more in a bit at a time until the consistency is right. Try not to overwork the sauce. Sir in the bacon (or ham).
It's now done, if the macaroni was hot. You can bake it for half an hour at 325, covered, then remove the foil or whatever lid and bake another 10 minutes or so to brown the top, if you like. You can also nuke or bake individual servings. Be careful: baking takes much longer than you'd think, and microwaving has a tendency to heat it unevenly so that one bit is blazing hot and another tepid. If microwaving, zap for about 3/4 the time you'd think, stir well, and wait 30 seconds, then test for temperature; if baking, a single serving will probably take 10-15 minutes covered at 325.
Again, make a big batch, as it reheats well. The sauce also freezes admirably.
Strain 2 cans of chopped tomatoes into a small saucepan. Add to the liquid small pinches of oregano and basil; I find that thyme and bay sometimes cause little kids problems. Add a generous pinch of sugar and a little white pepper. Heat this mixture over medium flame and reduce until quite thick.
Meanwhile cook chopped carrot, onion, and celery in a big saute pan or skillet in some olive oil (omit or substitute anything the kids really, really hate -- my son can detect quite small quantities of onion in things and until recently would often reject foods on that basis; he can now tolerate it, but he doesn't want to see it, which is OK in this recipe).
When the vegetables have softened, add the strained tomatoes and another pinch of sugar and perhaps white pepper. Cook, stirring, until beginning to dry out. Add the reduced tomato liquid and stir well. I find that it helps now to add 1/4 cup water and deglaze a little. Now puree the sauce -- a stick blender does this beautifully -- until very smooth, a texture little kids often like a lot. Adjust seasoning.
For meat sauce, cook ground meat -- a mix of pork and beef works well, and lean is good here -- separately from everything else until almost entirely gray, then pour off the fat. Add the pureed tomato sauce and cook over very low heat, stirring. At this point you can stop, but I find it's best to add 1/4 cup of milk, stir it in, and continue cooking very slowly until nice and thick -- a sort of pseudo-Bolognese. You can freeze this sauce, preferably in generous kid-sized portions.
To serve, just heat up an appropriate amount of sauce -- kids like a lot, I find. If using from frozen, just nuke it until it's hot, possibly stirring once along the way. Drop hot cooked spaghetti into the sauce, stir briefly, and serve the spaghetti with a big fork and spoon, then ladle the rest of the sauce on top. Add lots of grated Parmesan: my kids adore cheese, anyway.