Kids are hard to focus, yes. I have plenty of experience with that
Here's what I found that works well:
1-Set your max ISO lower in the ISO range. I set mine at 1600 in my K-r and 800 in my K20D. You find what works well for you.
2-Use Av and stop down the lens one third. That would mean f/3.2 for your 16-50 and f2.8 for the DA 35 2.4. F2 for the FA 31.
That way, when the light gets lower and lower, it will lower the shutter speed instead of just increasing the ISO (the higher the ISO, the less sharp the pic will look, even if you do preserve details with modern cameras).
Now regarding technique taking kids pictures, three things are important:
1-The direction of light. Some call it "stepping into the good light". The light needs to be coming towards the subject, not their backs. I know that this is obvious but I see a lot of people complaining that their backlit subjects don't look good and then they blame the equipment. So position yourself where the light is shining on their face. If it isn't possible, just wait a few seconds and they'll move and the chase starts again
2-Have the finger on the shutter half-way (for SR activation) and wait for that "pause" moment. Don't shoot when they are actually moving, unless you are in good light. Motion blur will rob you of sharpness more than high ISO. DSLRs are great in that there is hardly any shutter lag, my K-r in particular is so great with that.
3-Always focus on the eyes. Who cares if the ears aren't perfectly in focus.
I usually annoy my kids for only about 5 minutes at a time, tops (I think). It's enough to get 1-2 good shots of each in good light. Then we go on with our day until next time.
But the fact is, by doing this I get wonderful pictures even with my K20D (and DA 35 2.4) at lower shutter speeds (even down to 1/15 or 1/20 is common for me) when they are having a "pause" moment in good light.
I hope that helps