Yep, you can get buses and taxis most places on Lantau - Ocean Park is on HK island and there's now an MTR going there, would definitely recommend it over Disney.
The trails are reasonably well signposted but it would be worth at least printing off a few maps,'oat saw toons of the Lantau Trail would be walkable with a 10 and 12-year-old if it's not too hot, Hong Kong island is a little easier to divide into shorter hikes and the Dragon's Back is probably the best of them.
The outlying island are definitely worth a look too, Lamma has its charms and the walk between Sok Kwu Wan and Yung Shue Wan might be my favourite short hike in Hong Kong - though if I was to pick just one, it'd be my former home, Cheung Chau - it's like a busy part of Kowloon crossed with a Greek island and there's nowhere else quite like it on Earth.