Hello and
While it may seem extreme to build another coop, one cage is not enough if you have more than one chicken. Sooner or later you will always end up needing another cage, generally at the most inconvenient time and due to emergency with one or more lives at stake. I would recommend you put 'make/get another cage & run' on your to-do list. Plus, 'chicken math' will likely strike and you'll need that extra coop.
It doesn't have to be huge. It can in fact be tiny; say, just enough to house two tiny Silkies. I made some little coops with sheltered areas, small runs, etc where birds can temporarily live while brooding or rearing chicks, for example, and most of them I made mobile or they were mobile due to their size and weight. It can be so small you have to lift the lid to get to them, another cage and run doesn't have to be any massive undertaking, but it is a necessity. If your yard is big enough you can have the Silkies at one end and the big hens at the other. Left to their own devices, birds of a feather/ breed/ age/ clutch tend to flock together and will roam in isolated little groups of their friends and family only.
If you get rid of victims you're keeping bullies, so the problem of bullying is not solved. Bullying is often just a neurotic obsessive behavior we've bred into some lines, not actually based on anything justifiable nor comparable to wild animals; quite often the victim's only fault is that they were not able to strike back. In the wild bullying is generally due to the victim being ill or injured, but in domesticity it is very often just due to the abnormal mentality of the attacker, nothing to do with the victim.
The defining characteristic of bullies is that they make victims so as long as you have more animals the bullies will find someone to abuse. If you only keep bullies, they will even bully other bullies and you end up with a very aggressive flock. If you keep the bullies' victims though you can end up with a very peaceful flock, though some victims will reveal themselves as bullies if given a chance. Most don't though, but there are normal hierarchy squabbles and severe kill-attempt battles too and it's important to distinguish between the two. Bullying is based on a mindset which you are unlikely to be able to alter in their lifetimes. In this case I would guess your adults are bullies as I highly doubt any 2 month old Silkie is offering fully grown large fowl hierarchy dispute challenges.
Depending on the severity of the bullying, you may be able to help settle things. But if they're chasing the Silkies, going out of their way to attack them, you're best off removing the Silkies for their own sakes. That's bullying and left long enough it can result in death or maiming. Some chickens will be so stressed by bullying they stop eating or their immune system becomes weak and they die from illnesses they should have survived. Stress is potentially a killer.
In this case, you have two adult and laying hens who have suddenly been put into a new situation along with two weird and fluffy children. Moving to a new situation alone can provoke a hierarchy reshuffle. As well as that, adult chickens rarely actually like living with 'children'/juveniles that aren't their own, and even if they were their own chicks they'd likely be less tolerant of them at this age. The weirdness of Silkies and their hairdos, preventing them from easily seeing alphas walking up behind them, makes them prime targets for most 'normal'-type birds, as they not only look weird but act like they're blind or rudely oblivious to the alphas. They often get treated like the freaks they are among birds not used to them. If you were told they get along but they're not, it's unlikely that this just started now. Maybe the other person's idea of 'getting along' is 'well, they're not dead yet, so...'
Anyway, I think your best bet is just to make some other little pen for the Silkies and have them sleep elsewhere. They may be able to free range during the day in the same yard as the others without interference from the other hens; sometimes laying hens don't want to share coops with unrelated individuals as their instincts may tell them to clear the territory for their own future chicks. The coop is 'home' territory, not neutral ground. Whoever is currently alpha owns it and considers it home. Everybody else is there on sufferance.
Best wishes.