Having the dogs fangs trimmed won't solve the problem, could be costly, but may help prevent injuries so I would consider it if your vet recommended it but hold off on that one for now; for me that would be a last resort.
I have to say first NEVER try to break up a dog fight! I know it might be hard to let them do it but you could get bitten and severly injured in the process and I am supprised you haven't been yet! That is a very dangerous situation to get into!!
Second, get your dog spayed! This greatly helps with aggression among other things. Here is a web site for you to look at:
Why You Should Spay or Neuter Your Pet | The Humane Society of the United States
Third, always keep the dogs separated especially at food time. Do not leave food out or give treats that take a long time to chew such as bones or raw hides. Only small treats that can be eaten quickly. As soon as the dogs are done eating take the bowls away. Be careful of food agression becasue they can be aggressive towards you too if the behaviour is not taken care of so make sure they are away from the bowls when removing them. If you have the dogs together maybe have them muzzled and on leash with a choke collar in case they start becoming aggresive, then when they start becoming aggresive you can quickly gain control by pulling the leash so it tightens and holding it away from you while saying loudly NO; this is in extreme cases when they might attack. This was recommended to me by a trainer when I had problems with my dog.
Fourth, take them to a trainer/behaviour specialist right away. This problem needs to be handle right now before it escalates and anyone else or dog gets hurt. The trainer can work with you one on one at their facility or come to your house and give you specialized training. It's relativley inexpensive especially compared to vet bills you might have to pay!
It sounds like the mother is the instigater and the daughter is just trying to defend herself so keep an extra watchful eye on her to make sure other behaviours don't start.
Good luck!