A friend of our family highly recommends this motel for families. This is a link to the Taichung motel they stayed at. They have three presidential suites. Weekdays, list price is $4380 per night for the room.
Map & directions: http://www.o-wellmotel.com.tw/taizhong01/tz01_transport.html
You get a huge room with king-size bed, living area, indoor jacuzzi, warm outdoor pool, free wireless internet, KTV facilities, TV, and free instant noodles! (Extra bed/sofa available.)
From the site, it does sound like a place to romance your loved one, but my friend raves about it as a place to relax with your family. The kids can play outdoors while you watch them through the glass from the jacuzzi.
Here is the link to the Tainan motel: http://www.o-wellmotel.com.tw/tainan01/tn01_rooma.html
Map & directions: http://www.o-wellmotel.com.tw/tainan01/tn01_transport.html