Hi!
Unfortunately adding a third piggy (including a neutered boar) will not work with a dysfunctional pair; the newcomer will in my own experience soon side with one of the feuding piggies, which is inevitably creating an outsider situation.
Adding More Guinea Pigs Or Merging Pairs – What Works And What Not?
What many people do not know is that sows can also suffer from hormone problems during their teenage months, only that it rarely leads to a full-out fight. Have you considered having your bully girl vet checked by a good vet and discuss hormone treatment or a spaying operation?
Sow behaviour and female health problems (including ovarian cysts)
Before you make any further plans, please try to re-bond them on neutral ground. See how that goes; especially check whether the under-sow wants to be with her companion or is stressed out by being face to face. That would give your piggies their say in the affair and you can then make any further decision on a much more informed basis.
Bonding and Interaction: Illustrated social behaviours and bonding dynamics
Please never rehome a guinea pig into a single situation and if you rehome privately, make sure that you have visited the new home and any set-up in person beforehand; also that any new piggy company is working out.
If at all possible, contact a rescue within your reach with mandatory quarantine and vet care that does not adopt out single piggies, either. Ideally you date your other girl at the rescue to allow her to choose who she wants to be happy with if you can get to a rescue that offers dating. Age and gender (opposite gender de-sexed, of course) come a very distant second and third to mutual liking and character compatibility.
Please also keep in mind that as a caring owner, you will experience very strong feelings of guilt and that you are going through a full grieving process when you give a piggy of yours away, even in those cases where it is the best solution for a piggy and the new home is every bit as good or better than yours (whether that is privately or through a rescue).
UK:
Recommended Guinea Pig Rescues
Some other countries (including US):
Guinea Lynx :: Rescue Organizations
There are of course more rescues, but in these cases it is up to you to check the quality and safety of the individual operation as in English speaking countries anybody can call themselves as rescue without licensing and welfare checks - and the results can be accordingly. The above links are all carefully vetted good standard rescues that comply with and surpass welfare recommendations at any stage of care in rescue and the adoption process.
Your dominant girl may most likely be happier with a neutered boar companion than a sow, and so may your under-sow, especially a gentle adult one.