This is a difficult situation to be in. I think first and best is to let them work things out between themselves and avoid being put in the middle. I can't imagine any partner hating another, but I am sure it happens in some relationships. I can see how one might greatly dislike another, and that is very unfortunate. Again, I would encourage them to work things out between themselves and try to avoid being pulled apart by the two of them. Sometimes, especially if one or both, are mistreating the other/one another, I would think that is the time to step in and say "whoa, hold on there" as not stepping in, this "mistreating" is, in my opinion, abuse, which is NOT o.k. at all..
If the two cannot work it out, then I would suggest family counseling. One partner trying to mediate between the two having the problems with each other could really make the situation worse. There is the possibility of the mediator taking sides, or the other partners feeling the mediator is taking sides. I believe it is best to handle this straight forward and nip it in the bud...as I think mistreatment might lead to actual feelings of hate, which is destructive to all involved. Airing things out with a 3rd party who is not vested in the relationship can greatly help. Anger, resentment, jealousy, dislike and hate can be vented in a safe place and left in the counselor's office, rather than having it spewed in the home. Especially if there are children still living at home, regardless of their age...minors or adults.
When we were in a poly relationship, we had a "Head of Household" (HoH) relationship, so I had the final say/word in any matter if there were to be a deadlock. I know this is not the ideal for some, and may not work if even one partner chooses not to follow the guidelines agreed upon for the relationship; ie, one partner having the final say. But I could not just say, "Stop hating or disliking one another"....it just doesn't work that way. I could however say, "There will be no more mistreatment of one another" and expect that to stop and then work on ways of communicating in a positive manner.
Maybe others will disagree, but I feel "mistreatment" is a form of abuse, they are not seperate and different things. So it is extremely important to NOT let the situation fester and go unaddressed. It will only get worse. My thoughts here are just that, my thoughts...so if anyone else has some other ideas, please post, as this is a serious matter in any relationship.
May we all live in love and not tolerate hate or mistreatment/abuse of anyone.