For the day of arrival, be very very careful of the 'rest' option. Falling asleep runs a risk jetlag setting in and that could wreck the rest of such a short stay. Relaxation is fine, sleep is a real problem as if you do that for the morning you will be 6 hours out of sync....believe me that 6 hours of being physically worn out is far better than 4 days of stupor from jetlag. The sort of things you have listed are fine for the day of arrival - minimal concentration required, plenty of places to sit down etc. I would start earlier - late afternoon depending upon exactly when you mean (for me that is 4-5pm) would leave enough time to see the Gardens. Better to keep moving and see them and then have to crash out early evening....especially since you need to be functional for the next day
The 26th is a long day - the River Safari and doing everything took me 4 hours, I do the zoo from 9-4 despite having been many times and that doesn't involve more than one or two feeding talks and normally no shows which as a first time visitor you may wish to do. This is a 10hour day to see fully - at least. I certainly would not be adding anything to this day other than dinner. Its a heavy day after the day of arrival and I would possibly suggest swapping this day with another lighter day just to get settled in Singapore before a big hard day - and this one is the heaviest that you have planned.
27th seems a major waste of money for just one or two rides unless they are icons to you. There are options outside of USS for rides to satisfy the thrill seeker - the Luge, and the Zipwire are just two that could be a replacement if you are not going to do USS justice. Or you could split the group if one person is interested and the 9 year old and someone go to USS and others do something else, then meet for the rest like SEA.
For the Science Centre it is a good half day - from opening time to about 1pm as a basic figure - more depends upon if you use the water play area for kids, or if any temporary exhibitions are of interest, or if you plan to expand to the IMAX cinema or similar - and of course the flight time. There are no lockers at the Science Centre from memory so you have to think bags as well.
