We had a simular problem some years ago, what I did was look at the pack system, both of my dogs no that I am top dog, both myself and wife are in charge (very important on a NB) dogs want to be with the pack/family in the central living area, try if you dont already have one get a dog cage, only need a smaller one for your breed, put it in another room and which ever one starts first put it in there, it may go crazy, be strong and let it calm down, then when your ready let it out, lots and lots of reward for good behaviour, dogs hate being shut out of the family/pack, it may take a while but should firm who is in charge.
Keep both dogs on the floor, if one is on the sofa for example it can see its self as higher up the pecking order, both ours are not allowed on furnature. Nutering does help but can take a while to notice a difference as hormone levels can take a while to drop. Also if you have a cage you no you can keep them safely apart incase of an
emergency. This helped with ours and they get on fine, but I always seperate them when we go out. Hope it helps!