Help! Cat attacking other cat

[CinemaPantomime]

I have 3 cats. All neutered.
First is a female aged 6 - she was a rescue who my DM adopted and I inherited 4 years ago when DM died. She can be very sweet but is a biter (to humans, without warning) so we have to be wary. She's goes outdoors.
Next we have 2 Burmese. A very large and docile boy, and a very small needy girl. They're indoor cats. We've had them for almost 3 years from kittens. We got the Burms because the rescue cat isn't the best pet for our children but we all do love her and I promised my DM she'd always have a home with us and she will. The Burms are the children's cats.
The trouble is that our Burmese girl (BG) is bullying the rescue cat (RC) horribly. RC isn't a fighter at all. She's never been fond of the 2 Burms but they rub along and will often all sleep in same area such as on our bed. The Burms try to play with RC but RC isn't interested.
After almost 3 years BG has discovered if she chases RC, RC will run. We intervene. This chasing has developed to BG attacking RC recently but we were unsure how malicious it was. We discovered RC had an injury a week ago and she's been to vet and had abscess drained and just finished antibiotics. When she was shaved vet found another old bite wound too. We thought both happened outside as there's a local bully cat but had a suspicion it could be BG.
We've kept RC and BG apart for last week except under supervision. All seemed fine but while I popped downstairs today I heard some charging around and rushed upstairs to find RC cowering in a corner scared witless with BG ready to attack again and clumps of fur around.
I'm now thinking BG is responsible for RC's injuries.
This is new behaviour.
I'm at a loss what to do. Clearly I can't leave BG and RC together at all without supervision but that's hard long term. Has anyone had similar and how did you fix it? We kept them apart for a week except under supervision but the second I wasn't there BG has attacked and cornered.
Any ideas please? Feeling upset for RC. BG only seems to do it if we're not in the room.
Any ideas welcome.

Cats are highly sensitive to smell. Other cats in your RC territory could be stressing her too.
Mine tend to kick off with staring and funnily enough it's incredibly easy to de-escalate, I simply put a box or similar in their line of vision and that's usually enough to stop it.
I usually have a Feliway friends running, but if my older cat seems a bit more jumpy I will get the standard one for a little while too and that seems to smooth them all down.
I had a male oriental before and they were very close, used to groom each other and sleep together so it's a shame that the newbies have not jelled in the same way. However I am glad I got 2 as they generally keep each other amused.

I suspect it started with chasing as RC began running - only recently though. Before that she stood her ground and BG would wander off. Since RC started running I think BG has gained confidence and it's escalated.
Now have bought 2 feliway optimums off Amazon, will continue with separation for now, and will start providing more hidey holes inc lower down where RC tends to stay. A bell for BG too.
If it's the vet smells spooking BG hopefully that'll all help with time. I think we can keep them separate long term if needs be due to house set up but it's not ideal. It's possible though.

Also have been looking into secure fencing for garden.

That all sounds positive. I think the dynamics can change with cats but can keep changing, so don't give up hope. If my older cat runs, the others chase her, but if she doesn't, they immediately back down. I think she is naturally a flight animal though, so standing her ground is brave.
There are tips online for introducing new cats which I think also work well for existing house mates being a bit fractious. Cats often live in colonies when feral so it's entirely possible to have several living together, but you do need to ensure they have enough space, resources and safe places.

Yes will start reintroductions after feliway is in effect. Also considering Zylkene or Royal Canin calm but would talk to vet first.

I have read that if one cat goes to the vet and one stays at home the returning cat will smell wrong and may not be recognised- just treated as a strange cat never encountered before.

I can recommend Feliway Optimum as well. My rescue cat suffered from OCD before I adopted her; she was overgrooming which stopped when I got her.

A couple of months ago, she suddenly started to overgroom again. I took her to the vet to have her checked for any medical reasons causing the overgrooming. She was fine besides her urine having a slightly raised ph level for which she is taking medicine to acidify her pee. That, however, did not stop the overgrooming so I bought the Feliway Optimum even though I didn‘t really think it would make a difference. It did and Micky‘s fur is now intact again.