Transportation from HKIA, i have some clarifications:

As for your questions, here are what I know:
1. That's right. You need to buy Octopus Card for your kids and there is special card for kids between 3 and 11 years old.
2. You can take airport shuttle bus no. A31 and get off at Chung On Street bus station, which is very near from your hotel. So you can walk there then.
Besides, there is another way for you. The hotel provides shuttle buses that pick you up from the airport to the hotel directly. It costs 120HKD per person.
3. To Disneyland Resort: walk from your hotel to Tusen Wan MTR Station to take subway Tsuen Wan line to Lai King Station, where transfer to subway Tung Chong line to Sunny Bay. Then upon your arrival at this station, it is easy to find the Disneyland Resort Line, which can take you to attraction directly. For the back journey, you can also use the same way.

To Ngong Ping, as the way I mentioned above, after getting Lai King Station, you can transfer to Tung Chung line to its terminal - Tung Chung Station, from where you can walk about 5min to the cable car station. Then take the cable car to Ngong Ping and Giant Buddha as well.

After visiting Ngong Ping, you can get back to the cable car station by cable car. Nearby you can easily find bus no. 2, which can take you to Mui Wo Bus Terminus, near which it is suggested to take a ferry to Central. You may get off at Central Pier no. 6. Then walk to Central Pier no. 7 to take bus no. 629 to the Ocean Park directly.

Well, after your visiting at Ocean Park, take bus no. 629 back. Then walk to Garden Road, Central to take the peak tram to the peak. Afterwards, take the peak tram to Central and transfer to Tsuen Wan Line back to Tsuen Wan MTR Station, from where you can walk to your hotel.

Go on with my answers above:
For your transportation on D3:
The hotel provides shuttle bus to Tsim Sha Tsui and Mong Kok, both of which are recommended shopping areas. The Avenue of Stars are within walking distance from Tsim Sha Tsui Station. And you can enjoy the Symphony of Lights near Victoria Bay, which can also be reached by walking from Tsim Sha Tsui. Back to your hotel, you can take the hotel shuttle at Tsim Sha Tsui or Mong Kok as well. But you may need to reserve that in advance.

From your hotel to HKIA, you can use the same way I mentioned in the former answer. Well, if you wanna use the hotel shuttle, it is also necessary to make a reservation, at least an hour ahead.

Thank you

Thank you Gloria. I feel like our Day 2 itinerary is too tiring. Please give us again your suggestions and directions to and from our hotel. What if Day 2 will be Ngong Ping, Giant Buddha and shopping (please suggest areas to visit) then go back to hotel. Then Day 3 will be ocean park, the peak, avenue of stars and symphony of lights. Thank you for your patience.

If you think the D2 itinerary will be too tired for you, I think your plan is pretty well. Following your plan, you can enjoy every place freely and pleasantly.