Agree with the others, if the nest your bun is making looks reasonably safe, the best thing to do is to let her carry on with the location she’s chosen (and not sit in that seat for the next few weeks for safety’s sake). If she’s built the nest and pulled fur, her kindling time is likely quite close. She’ll probably give birth in the nighttime hours (which seems to be the favorite time of day for rabbits to bring their kits into the world), so the first indication you’ll likely have of the new babies is when you go in to check how she’s doing and see movement in the nest. At that time, as Josip says, you may be able to move the babies and their nest to the nestbox.
As Josip and Mikey say, check them once a day after the first day to see that they’re OK; they should be warm, snuggled up together in a cute little pile, with plump bellies translucent with milk, and wriggling around or sleeping soundly. They should have their fur start to grow in within a few days and generally their eyes open and ears go up about (I think) 10 days or so after they’re born. By 2-3 weeks they’ll be totally adorable little fluffballs and you can start very gently interacting with them to get them socialized with humans. They should stay with their mother for at least 8 weeks (some say 10 weeks is even better) until they’re weaned and able to eat hay, pellets and greens and drink water. Make sure to keep the two adult buns (father and mother) separate; this is chiefly to prevent any further pregnancies, does can get pregnant again almost immediately (as in an hour or two) after giving birth.
You should check the other bunny (or get someone who knows to help) to see what sex they are; they should be spayed/neutered to prevent future accidents. The mother also needs to be spayed, though probably not while she’s still nursing her kits since she needs to be with them until they’re weaned (which goes right back to the necessity of keeping the two adults separated). By odd coincidence, I just adopted a mother-son pair; the mommy came to the rescue having just recently kindled four kits, all of which have survived and thrived, I’ll have to ask the Friends of Rabbits folks when the mother was spayed. The kits themselves should also be spayed or neutered when they reach sexual maturity.
Good luck!