Of course you want best for your rabbits and their babies, as I understand this is your first experience with babies so I just want to clarify some things here.
Firstly, your rabbits (parents) are not neutered/spayed, so they must be kept separately all the time, as you said you don't want more babies. The only way you can keep them together is to fix them both or at least one, who is more sexually active, after that after about two months after surgery you can try bonding them in some neutral territory, like bathroom, where they both never been before. It could take a few days to few weeks, after they are bonded they can live in the same enclosure/playpen etc, you have a very nice area for them, it's a pity that they can't play together.
Secondly, you say you want to keep one boy and one girl for each so they don't feel lonely. I'm afraid you won't be able to house father with son, babies are babies only until 3-4 months after that they will start fighting and marking their territory if there's another male rabbit. So you will have to neuter them both (and wait 4-8 weeks after that) before you can keep them together and there's no guarantee they will bond, two males are harder to bond than male and female.
So now is good time to start looking for good new homes (for boys at least), because if they are 9 week old you only have 2-4 weeks before they will start demonstrating their hormones, believe me it could be very challenging if you have 4 boys and father you will have to keep them all separately, no kidding, they will start spraying walls and marking everywhere with their urine because they will see and smell other males around. They will start circling and humping each other showing dominance then they will start fighting and can even kill each other. Also it will be more difficult to rehome them because they will be acting like teenagers, imagine someone is coming to meet them and they are spraying walls there and thumping and humping your hand and other rabbits. Now, between 8 and 10 weeks is best time when they show how sweet they are.
Girls can stay with their mother for a few more months, but also some females are very territorial and when they are 3-4 months there also can be fur flying and peeing on your lovely floor and walls, it depends of course, some are calmer and can tolerate each other until 5 months sometimes you can even bond mother with one of girls, but can be disastrous as well. Especially when it is your first experience.
Sorry for painting it all so dark but babies are changing really fast, best would be neuter your male asap and rehome babies before they start acting as teenagers, so you have 2-4 weeks from now. Try rehoming boys first as you will need too many cages to keep 5 males separately.
