I can think of a couple of variations of how this might be done. But since the rosary is not a liturgical prayer, there is no particular way it must be done.
I would imagine that that one group would do as you say and lead the first portion of each of the rosary prayers and either the second group or both groups will recite the second portion. It would be likely that they trade off leading the various decades.
It would make sense to me that a single person from the group leading the prayers would announce the mysteries but there is no special reason why the whole group couldn’t do so.
It’s also possible the the rosary could be chanted rather than just recited. I have no idea if there are any “standard” rosary chants.
All in all, it would probably be useful to look to how the Psalms are traditionally chanted communally, with the two sides of the church alternating couplets.
Attend any community’s Liturgy of the Hours (any hour) for ideas.
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