It is not so much an obsession as much as Ellen believes procreation will save both the humans and cylons, the Six’s believe it is the future of the cylon race.
Which is kind of true because otherwise the humans would die out, and there’s a fair chance there would be little to no innovation for no ideas thus rendering the cylons stuck.
Ellen see’s this and that combined with her maternal nature makes her desire children greatly. I believe the fact that she could not have them was why she began drinking and having…questionable relations with men outside her marriage. Even when she regained her memories she ,nor any other cylon, knew why the cylons could/couldn’t reproduce when they were basically human in the reproductive sense. She couldn’t reconcile that she would remain childless particularly when she and Saul claimed to be in love which was what they thought was needed.