Definitely look into a camping stove for boiling pasta etc. But also google slow cooker pasta options - this is quite popular in the US as a concept. This link came up on my first google (although haven't looked at the recipes: www.bettycrocker.com/menus-holidays-parties/mhplibrary/everyday-meals/best-slow-cooker-pasta-recipes).
Will your kids accept noodles instead of spaghetti? Most of those asian noodles are like couscous - they only need hot water, not to be boiled.
To cook vegetables in the microwave, place in a bowl with a few teaspoons of water, cover in cling film, prick it and nuke. For a bowl of carrots or similar I'd go with about 2 minutes. Alternatively, buy frozen vegetables and cook the same way - but saves you peeling and chopping. Tends to take a bit longer to nuke. Sweetcorn should be wrapped individually in clingfilm. Two will take 3 minutes. 3 will take 4 minutes and 4 should go in for about 5. Leave to stand for at least 2 or three minutes after - longer is fine too. Broccoli, asparagus and other more "delicate" vegetables may take longer. Spinach can be wilted in about a minute. (I regularly do lunch at the office with a piece of hot smoked salmon, half a bag of rice, wilted spinach and some creme fraiche, but it sounds like your DC wouldn't go for that).
Definitely stock up on bag rice - so much easier. Ditto, new potatoes can be nuked too but again, you'd probably have to experiment to get the right amount of time. I'd think about 5 minutes or so, but possibly longer.
If you do a large bbq, wrap jacket potatoes in tin foil and place them on the edges of the coals once the flames have gone down (but before you're ready to cook your meat). You can do this with sweet potatoes too .They will take probably about an hour to cook. Do enough for more than one meal then you just have to nuke them slightly when you want to heat them up later.
What do you mean by dry meat? If you mean meat that hasn't been pre-browned, yes. The BBC good food website was doing some specials on this recently. Take a look at their website. It you can afford it, consider buying bags of prepared vegetables for the slow cooker, or use frozen vegetables and increase the time you use to cook them (I haven't tried frozen, but imagine it would work fine).
Also things like mince for spaghetti bol actually works very well in the slow cooker and doesn't require pre-cooking if you can't manage it. Just throw your onion, mince, stock, tomatoes etc into the slow cooker and leave to do its thing over a long long time.