If the white buck and the white doe have pink eyes, they are the color we call Ruby-eyed White (REW). If you breed two REW's together, the only possible color their babies can be is REW. If you had babies that were any other color, they didn't come from a REW x REW breeding. I'm guessing from your description that one doe is what we call a "broken;" some color plus white, typically in a pattern that puts color on the ears, color around the eyes, color on the nose, and some color on the back, either as spots or as a larger patch called a blanket.
If there were broken-patterned babies in the first litter, then yes, it follows that the broken doe was the mother. As I said, if the buck was still in the cage when she had them, there's a good chance she is pregnant now. She might not be, but at least you have the head's-up so you have a chance to be prepared, if she is.
A wild rabbit doe digs a burrow in which to have her litter. We don't usually give her domesticated sisters the opportunity to do that, but we need to provide them with a safe, secure, closed-in space that simulates a burrow; most people use a nest box made of wood or metal. Baby bunnies are surprisingly mobile, and the box helps to keep them together. Sadly as you've seen, if they wander away from each other, they can chill and die. Almost all does lack the instinct to put babies back if they get out of the nest, probably because the shape of a natural nest itself keeps them together.
During the days just before kindling, the doe gathers nest materials. Normally, this is plant material; we usually give a doe hay or straw. The hay helps to provide some insulation, and also absorbs some of the urine that the babies will produce. If there are other rabbits in the cage with the pregnant doe, she will probably pull hair off of them; I remember one family that was very confused because most of the fur in the nest with their new litter came from their buck (he was a different color than their doe).
Even people who are trying to raise rabbits in colonies often find that putting a pregnant doe in a space by herself is the safest thing for the babies. Sometimes, more than one doe will try to use the same nest box for their litters, and the babies in the first litter get injured or killed by the second doe's preparations for her litter. Does can be very territorial, and squabbles over nesting and resting sites create unnecessary stress on a pregnant or nursing doe, which may lead to her abandoning or killing her own litter. I hope y'all figure out ways to get these rabbits settled into some sort of order that makes things less confusing and stressful for all of you - I know dead baby bunnies are no fun.