What's the verb for swinging the skipping rope so that people can skip over it? For example: "They were ___ the skipping rope so that their sisters could skip over it." I am not sure, but swinging is too general, because it doesn't imply a rotating motion.
The term used in competitive contexts seems to be "turning":
In competitive Double Dutch, there are two types of teams–a single team with three members (two turners, one jumper)
the second jumper exits the ropes, takes the ropes from the third team member (who has not yet jumped), and becomes the turner
Swinging is fine. If you need to say it was not just going from side to side you could use spinning the skipping rope. But "holding" is probably enough in context
Jak and Maz were holding the skipping rope while Katie skipped. A line of children waited in line for their turn in the middle. Jak spun the rope faster until it caught Katie, and she glared at him...