Kits can generally survive when weaned at 4 weeks, but the consensus among the breeders I know is that giving them 6 weeks is a lot healthier. I leave mine in for 6-8 weeks, sometimes a little longer if I'm tight on growout cage space.
Some does love on and feed their babies for months, but by 8 weeks the mother is usually
totally done and alternates between sitting tucked up with her eyes closed dreaming of being alone, and running away from a pack of insistent (and large) adolescents who still want to nurse. Also, the cages tend to be pretty darn crowded by then.
They really need to be away from mom and in their own cages, or at least separated by sex into growout cages, by 12 weeks. Because they can - I'm speaking from experience - breed at that age, and that's not just small breeds. I had a satin that became a sire at the tender age of 16-1/2 weeks of age, meaning he bred the doe at 12-1/2 weeks of age! I have noticed that the smaller breeds generally do get interested in reproduction a lot earlier than larger breeds. I always had to separate the Mini Rex at 6-8 weeks because the little bucks just wouldn't leave their littermates alone. Polish aren't quite so bad, but they still start bugging each other earlier than my Satins, Rex, Californians and New Zealands usually do.
It doesn't really matter if they bug each other in grow-out cages of males or females...unless you want to show them. Then you need to worry about them damaging each other, for instance nipping ears, nipping noses, barbering (chewing on/eating each other's fur) and biting. Bites usually heal fine, but serious ones can either leave a visible scar or change the color of the hair growing there. Rabbits will sometimes grow white hairs in dark fur where there's been an injury to the skin, and brokens or himis will sometimes grow darker hairs in white areas. In brokens that's not an issue but in himis it's a DQ (disqualification) to have either a white spot in a colored area, or a dark spot in a white area.
So, I usually try to separate my show prospects as early as possible. Sometimes I'll leave two keeper doe littermates together for a while if they seem to enjoy each other; it seems to make the transition a little easier. But even does that get along will engage in dominance behaviors, and you'll see occasional chasing, nipping and fur-pulling. When I intend to show one or both, I separate them fairly soon. If possible I put them in side-by-side cages so they can still interact without tearing each other up. But even then, I have two layers of separation and I watch them, as they will sometimes chew each other's fur through the wire.
The other reason to separate your show prospects is that rabbits naturally have a dominance hierarchy and some of that involves what's known as "guarding" behaviors. These revolve around food and water. It's subtle, but the lower-ranking bunnies are prevented from having at-will access to food and water. I have frequently found that bunnies which are the smallest in the litter really fill out once they're in their own cages.