Its not just the tent burning a fair few a year die due to CO poisoning. Very silly thing to have going in your tent.
Take a look at something like LOGIK L15CFS10 Ceramic Fan Heater. It does not get red hot so should be fairly safe with kids. I have the previous model and it keeps an 8 person tunnel tent toasty warm when required.
For my money if you need a heater when camping then camping probably isn't for your family unless of course your dragging them under canvas poorly equipped in the middle of winter! If this is for your summer hols then I'd give up on camping they will only find something else to moan about!
Tend to agree. With well insulating clothing and layered up, moderate cold shouldn't be an issue at all. For my GF, when we have gone wild camping, she has a Nalgene water bottle (will hold freshly boiled water) wrapped up in a piece of clothing acts as a good on-the-fly hot water bottle to cuddle.
Just get a cheapo convector heater, and you'll find it does the job marvelously. http://www.screwfix.com/p/ch-2000m-turbo-freestanding-convector-heater-750-1250-2000w/6270p The exterior doesn't get too warm, so you don't have to worry about burning children or melting bits of tent. They produce heat much quicker than an oil filled radiator, but they don't retain the heat after being switched off. But the answer to that is to just leave them on.
Do you already have the required cabling for using electrics? If not, then you'll need something like this. Sorry, just saw your post saying you have. Then, be mindful of the current draw of any electric heater you buy. If you simply buy a household heater of a few kW it'll be more likely to overload and trip the site (not the whole site, just your hook-up), especially if you have other stuff in use, e.g. a kettle. If such a heater had variable output, then I suppose you could keep it low, e.g. under 1000W. We don't use a heater, but have cool boxes, kettles, chargers etc and have to be careful to keep the Amps low.
I parked our caravan right up far end of a field like you - no one within 200 yrds - went out - came back to find another caravan parked 3 ft away and they had two screaming kids - was not amused.
There were no other campers during our stay, field was fairly wet in places and not having electric puts a lot of people off. I hadn't realised that the other side of the fence was a public footpath fortunately it wasn't used much otherwise I would have moved. I stayed on a small field in Scotland, we came back from a day out to find two caravans had parked up either side of us, it wasn't a big field but there would have been enough space for them to be further away! We left the next day.
I have a small vw campervan and use a small oil filled radiator when I'm near an electric hook up. It costs £15 from some cheapo shop and I've had it a couple of years. If you have hook up it's the easiest solution.