Having come here with a husband working for Cathay myself, I may be able to shed some light for you. I am actually still living in the Headland now.
Accommodation... During the time you are here for the interview you get to stay at the Headland for the 4 days or whatever they pay for for free. After that/or before you can stay at the Headland for a very discounted rate. Truthfully the Headland at that discount is going to be a way cheaper place (and probably nicer) than you would find to move to another hotel in Central unless you are looking to spend considerably more. When we came for the interview we stayed here at the Headland the entire time and it worked out OK. The bus you take from the Headland to Tung Chung (the closest subway station) is the S64. With the bus ride and then train central (Hong Kong Station on the Orange Line) is probably about 45 minutes away from the hotel. Nothing here is a bad commute since the MTR is such a great transportation system. It is 200 times cleaner and nicer than NYC in my opinion.
As far as looking at housing... You get 6 months to live in the Headland Hotel if he gets the job, and the company will set you up with an agent to help you look, so there is really no big hurry. Also, I understand price range to be very flexible up to a fairly high amount so I wouldn't be too worried about that. The company just has to approve the place and amount. I can understand wanting to check out the options though. We did the same. To see Discovery Bay, which truthfully with a family may be your favorite, you can simply jump off the first stop you come to from Tung Chung on the MTR (called Sunny Bay) and take a quick bus ride in to see the community. You may also want to check out other areas but seeing DB and the Mid-levels will show you some diversity. From Central you can walk up the Mid-levels Escalator to see the area there. It will be much more of a city life than Discovery Bay but is also a big expat community. Other than that, many Cathay pilots seem to want to be in the new territories. For me that seems like such a way of avoiding the really beautiful city life here. For the new territories you may want to see Sai Kung, but that might be too far for your visit for the interview.
As far as the sightseeing goes... Pick up Frommer's Guide to HK before you come. It is an excellent took to read and decide which things you will want to see while you are here. Since you will be staying on Lantau Island I would recommend a trip to the Po Lin Monastery to see the temple and have a traditional lunch. Also the new Sky Rail is open which you can ride up there from Tung Chung and see the sites on the way up.
As for part time teaching... I can't offer too much advice on that except that with a dependent visa here you will be legally able to work with no company sponsorship needed so you shouldn't have trouble finding part-time work.
Feel free to send me a private message if I can help you more. Tell your husband good luck with the second interview!