I haven't read the series, but from the descriptions I think you may be looking for Poul Anderson's Harvest of Stars series, published in 1993. A quick glance through the first book does have a lot of the action taking place on (in) an asteroid.
from the Amazon page:
Winner of seven Hugo and three Nebula Awards, Poul Anderson is one of
science fiction's supreme masters. In "Harvest of Stars," his most
ambitous novel to date, Earth lies crushed in the grip of
totalitarianism.To save her planet, his heroine, Kyra Davis is sent on
a mission to liberate our last bastion of freedom and rescue its
legendary leader. Her bold adventure will sweep her from Earth's rebel
enclaves to the decadent court of an exotic lunar colony, from the
virtual realities of biotech and artificial intelligence to a brave
new world menaced by a dying star.
On the other hand, your description could also fit Poul Anderson's New America, published around 1987. But another quick glance doesn't show any asteroids.
from the GoodReads link:
The benevolent, paternalistic World State regarded the freedom-minded
Jeffersonians as a minor embarrassment whose violent elimination would
cause more disruption than their demise would merit. So both sides
were happy when the chance came for voluntary exile to a distant
planet. But two hundred years later the less benevolent descendant of
the World State that had let them go was to decide that the cosmos was
not big enough to hold both it and a free people.