Loathe to interrupt another man's GAS, Mgoblue, but technique is super important. You could be given a sports photographer's D4 and 300 f2.8 and not nail toddler shots.
You have a K-50 and Tamron 17-50? I've shot cyclists with a K-30 and Sigma 17-50 coming towards me at 50kmh.
The key in AF-C mode is to be proactive, and not pick up your camera when you see one of the brood suddenly being cute! Get a good position like a sniper and track your subject. The first pic has to be already in focus - see the green square beforehand, hear the beep - then keep the shutter half-pressed until the Decisive Moment or you want to fire a volley of shots - or the rest will suffer playing catchup.
The subject might run behind a chair or another kid might cross the line of fire in front of your subject, which is why for me I'd be using Back Button Focus. Again, good technique, rather than maxing out your credit card.