Sorry that you have had such a stressful time arranging your travel (and that both companies' customer service is so utterly pathetic)!
There is no way that they will let your 2 year-old sit on their own (although as I read your post the thought did cross my mind that if I could leave my 3 year-old verbally entertaining two other adults for hours on end I'd be booking a long-haul flight immediately
...)
On the baby front I have heard very mixed things about the usefulness of the bassinets (people seem to say they're mainly useful for stowing your wipes etc within easy reach). I would take a soft sling to ease the getting on and off (and for when you need to sleep) and lie them flat on your lap when you're fully awake. A friend just travelled to Perth solo with a small one and I'm sorry to say she didn't sleep at all (but the baby did).
Wishing you all the best for your flight and a very Happy Christmas at the other end!