Does she have that much of an influence though? Berelain has in my opinion 5 important roles in the story.
1. Trying to seduce Rand.
2. Stewardship over Cairhien.
3. Chasing Perrin
4. Providing troops and some moral support during the hostage crisis
5. Romantic “target” for Galad
1 and 5 could be scrapped outright without loosing anything. If you really want you could replace her in 1 with some unnamed woman who just appears just once.
For 2. you could just have Dobraine be the steward from the beginning IMO.
I have made my opinions about