does have two different uterine compartments, so a doe can accidentally get pregnant in both, and if so it can really cause problems. HOWEVER.... her having the second ones a week later, means she was rebred a week after the first breeding and got pregnant on both. One of your children (or someone) put the buck back in with the doe a week later, OR the buck got her through the cage wire (yes they can do that). That's the only possible way were the second kits fully formed? If so that's the explainatino. IF they werent fully formed then she was bred earlier and aborted them because she already had a nursing litter. It can kill the doe so its' not suprising taht she's not doing well. If you have children that play with yoru bunnies you may need to ask which one may have let mama play with papa a while back.
as for her not eating...that's life threatening, if that was me i'd rush her indoors and force feed her a liquid mash of her normal feed and oats. Rabbits need food on a constant basis so a food strike is death waiting to happen if you aren't able to force her to eat. Iv'e force fed many rabbits, and over half regained their strenght and need to eat on their own...the others well died.