
Those very experienced with Staffs never leave two unsupervised together.
They have short fuses, and once a fight breaks out, (can be over the least thing), they will rarely back down, their roots are as a fighting dog, (the terrier part gave them the fire and willingness to fight, the bull part is the tenacity) and this is rarely too far beneath the surface.
Your younger bitch at four has reached social maturity and is simply trying to depose her mother. They do not see each other in the same family sense, just as rivals.
Chances are this has been building without you noticing for some time.
You only option is to manage things so they do not have the opportunity to fight. This will probably mean keeping them entirely separate as the younger has already resorted to seriously damaging the elder.
Baby gates, separate areas of the garden etc, depending on what is practicable.
Spaying rarely has any effect at all on the behaviour of fighting bitches, as it is not necessarily a sexually related thing, unless occurring only when in season, about to come or finished a season, with the rare very hormonal bitch.
There is some evidence to suggest that spayed bitches having the softening hormones removed are more likely to be aggressive.
I would of course have both adult bitches spayed if they are not breeding candidates to remove the risk of Pyometra.