This is a very peronal decision but my advice is absolutely stop over!
When we have flown to Europe with our kids we almost always stop over and only 1 time did we go striaght through. It was the worst trip by far. I try to get day time flights and find that the short break is a welcome relief from the tedious plane trip. Immigration formalities in Singapore are so fast that you will be sitting in a taxi on your way to your hotel in no time. No need to worry about that.
Make sure there is a pool and something interesting close by so that you can relax or sight see or sleep or whatever you need. I love my stopover time and consider it to be a vital part of my holiday. I don't think of it as time that I'm missing from my destination at all.
The time that we had to continue right through we certainly had tired and cranky kids - but we were stuck on a plane for another 14 hours - then when we finally arrived everyone was so exhausted the first day was completely wasted anyway. I find that with a stop over you do the resting before you get to the exhausted point and arrive feeling so much better.
Edited: 5:23 pm, March 20, 2013