Are you happy to eat dairy, just reducing the meat content of your diet - or do you want to limit dairy as well?
And are DP and DS picky, as in will only eat plain meat, 1 veg if pushed and boiled potatoes, or lots of fried stuff - or want a large amount of meat compared to the veg but will have pasta, curries, thai, morroccan etc?
I eat quite a few things that are either veggie, or reduced meat,
I do things like prepping a BIG batch of medditeranean veggies, diced up small (all same size) and marinated in some olive oil, balsamic vinegar, dried herbs, salt and pepper. Things like (whole cloves of) garlic, (halved) cherry tomatoes, (rest are diced to the same size) - mushrooms, courgette, peppers, (aubergine if you like them) etc. I tend to prep 2 courgettes, 4 peppers, 2 onions and the rest together - roast half (takes about 20-25 minutes) and freeze half uncooked for another night. Any leftovers can be frozen and added to a tomato sauce for pasta, with some prawns, sausages (chopped) or bacon lardons if you wanted an element of meat/fish. But the roast from the oven would often be served as the side dish to say a lamb chop/knuckle and some potatoes - which I tend to also roast for convenience that night. Goes well with chicken and white fish too.
Go for stew type dinners rather than 1 piece of meat and veg on the side. Add lots of veg to the stew - onions, carrots, squash, peppers, mushrooms etc - depending on the meat. While having some beef/lamb meals, do put a few chicken and fish nights in there too.
Veggie curries (Jamie Oliver did a nice one as an alternative to Friday night takeaway on a tv programme a few years ago that is very tasty and quick) are great. And even ones that include meat, you can increase the amount of veg in them (and take less meat yourself). Or do larger batches of both a meat (with some veg) curry and a separate veggie one, to eat one night, and freeze leftovers for other nights (lots of curries freeze really well). Or do a large batch of a meat one, with leftovers to freeze, and the next time, use leftovers for the boys and make a large batch of a veggie one for you, again making leftovers to freeze. So you only make 1 each time but can eat separate ones. Bulking out with veg, lentils, chickpeas etc do help to reduce meat content and improve healthiness of the dishes.
I tend to do my spag bol/lasagna sauce with maybe 3/4 carrots, half a courgette, a pepper and a handful of mushrooms chopped up in the food processor and added once the meat has browned before the tomatoes. And my shepherd's pie is similar except not using peppers (too sweet) but I do include frozen peas (whole) as well. My DSis uses a good handful of lentils in hers as well - I just can't cook lentils 
.
Similar to the veggie curry, we also do a veggie chilli at times. Its sloppier than chilli con carne but has large chunks of pepper, cauliflower, onion, etc and is surprisingly tasty.
The other option would be to do lots of stir fry type meals - a handful each of a few different veg - either with or without meat, and with different sauces to suit different veg/meat/carbs - so tomato sauce with pasta, cream and wine sauce with pasta/rice/potatoes, Chinese sauces with noodles/rice, curries, etc. Even starting with your veg and tomato sauce but changing the seasoning to make it Italian, Indian or Mexican works well.