The same thing happened to me - I thought I had same sex guinea pigs but was greeted with three balls of fluff in the cage one day just before Christmas. We too separated the male from the female and babies, but it was too late - she was pregnant again and gave birth to three more babies 10 weeks later.
It is very, very important to give the female an excellent diet with lots of calcium rich veggies and make sure she gets lots of vitamin C in her diet. You might consider syringing plain vitamin C to her daily for a while.
Guinea Lynx :: Diet
Make sure you are feeding all your piggies a high quality pellet (like Oxbow or Kleenmama's) as well as timothy or another grass hay in unlimited quantities 24/7. You can supplement mom and babies with alfalfa hay as well for extra calcium if you wish.
You should get yourself a good digital kitchen scale and start weighing mom and the pups daily to make sure they are not losing weight. The mom may lose a bit for the next couple weeks while the pups are nursing a lot, but then should start to gain again. You will have a chart showing her gains, and should be able to tell within a few weeks if she is really pregnant again because she will gain a lot of weight.
The pups will start to eat hay, pellets and veggies pretty much from birth. The more food they eat on their own, the less they will be taking from the mom's body, so encourage them to eat solid foods.
Any males will need to be separated by the time they are 21 days old - no later!!! You will need to learn to sex them yourself, and it's tricky with babies if you aren't experienced. You may wish to have a vet double check, but make sure the vet is VERY experienced with cavies, since they can make mistakes too. The best way is to check out this link on guinea lynx and do it yourself - check and recheck right up to the 21 day mark just to be sure.
Guinea Lynx :: Sexing Pups
We would love to see baby pics by the way!!!