I'm nearly speechless. Did this fighting just begin and your fiance has just begun hitting his son and be dogmatic about how you should discipline your daughter? I suspect that you and your fiance have been fighting about this and other things for some time and perhaps the tension between the two of you is influencing the children. How are they to learn peaceful ways of being with each other if their parent's haven't figured it out yet?
If I were in your situation, I would cut my losses. First, I strongly believe that hitting in this situation and in this way is counter productive to helping your children learn how to get along. And I would never stay with someone who showed so little respect for me and my thoughts that they would angrily insist that I do what they say. Disagreements are OK. Not being willing to discuss them and decide upon a compromise is not OK!
Unless he's willing to take a parenting class, or read a book or two about discipline, and then work with you, giving you as much respect as he expects for himself, while working out a discipline plan that you can both live with, I see no way of having this situation change.