1) Is it true that all hand luggage needs to be inside a clear see-through plastic bag? Where do I get there bags from? Do I need to pre-pack into this bag at home, or is it something I get at the airport?
It sounds like you got your information muddled, hand luggage can just be in a carry on suitcase/backpack and you can both take one case each on the plane, so you don't need to squish both of your stuff into the one if you don't have room. I'm sure you have read the link about liquids, but basically 100mls with a maximum of 1 litre each packed into a zip-lock bag. You can get the bags (1ltr) at supermarkets. They do have these bags at the airport usually, but I suggest you get the zip-lock ones before you leave and bring some spare in your carry-on just in case you get a leakage or a hole (not fun!).

Who are you flying with? Most planes have individual entertainment consoles at each seat and they are usually jam packed full of cartoons, movies and games for kids (with an old-style nintendo type of controller on the remote). Personally I would pack the laptop in your main luggage and not take it on the plane. The less you have with you on the plane, the easier it will be. Especially when you go through security you will need to take the computer out of the bag and it's just a real hassle when you're travelling alone with kids.

Also, big tip... If you don't have some already, buy some kids' headphones before you leave (leapfrog has a great pair, I think Target has them) and an adapter that will fit the plane's sockets (it has two pins). Not too sure where to get it, online perhaps? I bought my pair at Melbourne airport. The headphones on the plane are always too big to fit kids' heads and before I came up with this brilliant idea my son used to constantly complain that they kept slipping off.
They look like this:Amazon.com: airplane headphone adapter

One more tip, TSA locks for your main suitases!