We love Kathmandu. Its the most different place we've been (and we've been to a few!) and one of the few we've paid repeat visits to.
If I'm honest, I'm not sure I'd like taking small children to Kathmandu. The place is crowded - and I mean always touching another person when you're walking crowded. The air pollution and dust and dirt in the air is gross. We both end up with black noses for days after we come home despite using Buffwear things around our necks and over noses and mouths.
If you decide to go, I'd take the 3 weeks. The country is amazing. Chitwan national park has wild tigers and rhinos, and obviously the himalayas is fab. We did the Everest Flight on Christmas Day a couple of years ago and that was awesome. In fact, December is a nice time to go in the city - not too hot, not too cold - around 16 in the day when we were there so light jacket only.
We also went to a place called Dhulikhel, which is around 90 mins from Kathmadu and is in the hills - great if you like nature and walking.
The temples in Kathmandu itself are unbelievable. Oh yes, in fact another thing that may put you off with small children is the monkeys - they're everywhere and they're a pain in the arse. The hotel we stayed at was close to the crematorium on the bagmati river (which is worth a visit), which is overrun by monkeys. The hotel stated that no windows should be opened, as monkeys have been known to get in the rooms and steal belongings.
There is little western food around, so the kids would have to be adventurous eaters. We saw one Dunkin Donuts - no other chains at all. Reason I'm saying that it because, as an allergy sufferer, I know that in the majority of places in the world I can go in a starbucks, a McDs, something like that and definitely eat safely. Kathmandu isn't a place for that - everything is local food.May be an issue for children unless they're really good eaters. Unless you'd be staying at your friends house and cooking the house of course.
Overall its definitely somewhere that you should visit given the opportunity, however I'm really not sure about young children. The country is an amazing place and is in need of people visiting to keep money in the economy after the earthquake.