Singapore is a great induction to Asia in my opinion. It's uber-clean, everything works well, the food is great and so is the shopping.
If you can, I would suggest spending up to a week there - neither you nor the kids will get bored. Book it all in one stay and somewhere like Lanson Place would give you a very comfortable 2br or even 3br apartment with a cracking location and the added benefit of laundry facilities in the room. Note they have a 7 night minimum stay but we've used them twice as a family now and it's just perfect. Their shopping service will ensure the kitchen is fully stocked on arrival and you've got orchard road at your doorstep.
Borneo would work. I went to Kuching a few years back with my wife and the hotel arranged a tour guide for us. We did a half day at the Orangutan sanctuary and a full day in a nearby national park - you have to get there by boat & anti-malarials were advised so this may sway your decision.
If that doesn't appeal, Kota Kinabalu has a Shangri-La on the coast with its own orangutan sanctuary. Note this will push air fares up a lot though as it's twice as far away.
At that time of year for a beach you should probably aim for the East coast of Malaysia or Thailand. Why do you want a house? We stayed (again as a family of 4) in a hotel on the North coast of Ko Samui. 2 bedrooms and a living area, the hotel had maybe 15 rooms total. Was perfect for what we wanted. Oh, and the laundry was cheap!
For the temples I guess you need to aim for Cambodia or Laos - never been so someone else can probably explain far better what to do.
Asia is fascinating and you can make the ever weakening pound go a long way if you pick carefully (if you need to, that is). The temperatures and especially the humidity may be disconcerting if it's your first trip though and the 8hr time difference is worth giving some consideration to as well.
Kuala Lumpur is also good for a couple of days - some great legacy architecture out there and some bargain priced 5* hotels.
Research properly and you'll have an absolutely amazing time.