We're just back from a couple of years there and would go back in a heartbeat. It was FAB, you'll have a great time. People are very child/ family friendly and love to talk to foreigners as they don't get much in the way of tourists.
The weather there is done in extremes. DO pay attention to the news braadcasts when they say there is an ice storm coming, or a tornado THEY MEAN IT! We had a couple of hairy experiences within the first couple of months as we hadn't quite appreciated this! (A tornado sounds just like a train driving through your living room when it touches down 1/4 mile away from your wooden house FYI!) Buy a weather radio soon after you arrive and it will switch on automatically when any extreme weather is due so you don't get caught out if you don't happen to have the television on or don't hear the tornado alarms going off (they only go off during the day, not at night; WTF?!)
No rain showers as such, but random nights of torrential rain with spectacular thunder and lightning.
The winter snow is variable, some years there's lots or,like last year, a few disappointing sprinkles. Around the same time in December each year we went from wearing light trousers and short sleeves to -27F artic blast with a big dump of snow, which is quite a shock, but after the initial blast the sun comes out and it's a dry cold with no windchill so it's actually quite pleasnt.
I actually found the summer more of a challenge as they get 85-90F temps but the humidity makes it feel like 110F+. You can bundle a child up in winter, but the heat makes it a challenge to even get them from the car into a shop, and most of their shopping malls are totally outdoors, which bemused me. I went home to UK for a few weeks in August to avoid being mostly housebound.
Having read this back it sounds a bit negative, but dealing with the weather was part of the fun!
Housing is good quality, modern and large by uk standards.
Try to buy a 4X4/SUV as you will need it in the winter and when you go for driving holidays (St Louis, Mall of America in Minesota etc)with the kids you can all pile in with plenty of space. Getting around by car is so easy with sat nav, most places are only a few hours away, petrol &hotels are cheap, no point in flying. Also try to get a garage attached to your home or some kind of covered parking, makes life so much easier. We got car from car supermarket called Carmax as they would buy it back quickly when we needed to leave.
You can furnish your house in an afternoon by going to Nebraska Furniture Warehouse. A huuuuuuuuuuuuuuuuge place the size of about 3 aircraft hangars with everything you need in every style you can imagine. Pick everything up yourself out the back, or have it delivered the next day to your house, no 6-8 week waits here!
Don't buy anything at full price, there's always a sale.
Working in Kansas city, you can choose to live in Kansas or Missouri, we did both.
Anyway, I'm blethering now. Let me know what else you'd like to know about; I'd love to be going with you!