i think you should listen to the people in this thread cautioning against you seperating them too early. You do not have much experience with raising rabbits, and being that they were born on april 1rst is way too early. Be patient. these guys are just babies yet. they are just learning to eat their food. You can stress them out by taking their mom away from them too early. That can easily make them sick. Waite till they are six weeks old and then wean them. Some with more rabbit experience may wean early and it may work for them, but it doesn't work for everyone else. And its certainly not something all rabbit breeders do. Most wean at eight weeks because they feel its more humane for the kits to get the extra milk. breeding back heavily is also not a good idea. All it does is stress the doe and her reproductive system burns out at an early age. I also breed meat rabbits, and would never put any mine through that type of stress.
Do not turn them loose with your other rabbits either. Young babies set free is not a good thing at all and chances are you will lose them. Plus there is really good chance of them getting vhd since there is a new confirmed outbreak in the US.Also breeding back like that is never a good idea to do unless you have the proper setup to house the offspring in, and have an outlet for them. Like for meat rabbits, or pets. Otherwise you will end up with too many rabbits that you won't have room for. You can give her a break and breed her back 2 weeks after her litter is weaned. A lot of us that raise rabbits on here have outlets to sell them to for meat, pets, and show. Might be something you would want to look into.
Also if you are concerned about space try moving them to a bigger cage they can't escape from. Othwerwise leave where they are at for now. It might be a little cramped for them, but they will be fine. My babies are kept in cages, and they do tend to 'outgrow' them. But they are fine as long as they have some room to move around.