You can take a taxi or a bus directly between the two places.

Pauline, the Salisbury YMCA's website lists three options for getting there from the airport (express bus, taxi, or train). I'd be inclined to jump on the MTR's Airport Express line to the Kowloon station. Journey is a little over 20 minutes, so not too long if you're traveling with tired and jet-lagged young children! Once at Kowloon, you can jump on one of the free Airport Express shuttle buses or just hail a cab, as it's a fairly long walk from the MTR to the hotel. My experience of the Hong Kong MTR service has always been very positive, being very clean and super-efficient. Here's a link to transportation options on the YMCA's website: http://bit.ly/vniTty