AF on the 85 L II is slow. Certainly not fast enough to capture kids moving around. With the extremely shallow DoF accurate focus is very critical. I think this adds to the slowness of the AF as refocussing is needed after the slightest move.
It is not an easy lens to get good results with; it requires some time to get used to. S during your rental make sure you review your results regularly on a PC. In addition this lens really needs AFMA to get the most out of it.
5D3, 16-35LII, 24-70 2.8LII, 24-105L, 85LII, 70-200 2.8LII, 100L, 135L, 100-400L, 50 1.4, 40 2.8, Sigma 180 3.5 EX, 1.4x TC III, 600EX, 550EX