I would never try to divide a pulsatilla. They have a long tap root and lifting them almost always breaks this root causing the whole plant to die. Better to grow new plants from seed.

Agreed. And the best time to sow the see is when it is fresh. Personally I just let them self seed round the gravel near the mother plant and dig them when they are still small. If you want to sow them in pots then it is better to cut the tail off and just sow the hard seed as for some reason, the tail can cause the seed to rot.

That is exactly what we do OwdB - let them self seed and lift when small