First by forcing them to come to peace talks, then after whatever occurs from that exerting political and moral pressures and if the player is agreeable coronating the Inquisitor as having the support of the Chantry against the vileness of Lambert and his ilk and probably an opposing group of mages, not all rebelling mages, but I predict there will be an extremist group opposite the red templars. Lambert and Adrian should make fitting trophies for those who oppose the will of the Divine Inquisitor.
Sounds plausible. However, if the rumours about the peace conference were true, maybe that was her first attempt. And ended in disaster.
Although I can't see a schism happening, if the Divine dies, we may see a fight for the throne inside the Chantry (actually, that would give Cassandra and her Seekers a reasonable excuse to join the Inquisition, especially if the restoration of the Inquisition was Justinia's last plan to solve the conflict).
So we all think that while the more extremist elements fight, the more moderate members of each faction will at least attempt to reach a compromise.
Don't worry. The extremists' heads will end up on fancy Orlesian pikes
Kidding, but that was an actual option on the table before the Orlesian civil war.