Hi benji
Deary me poor you. This is not an uncommon occurance in over zealous mothers who may damage a pup when picking up or cleaning. I have several breeder friends who have three legged hamsters.
The pups are too young to separate from mum just yet. They need her to feed them still and keep them warm and clean.
Three legged pups do very well with a one level flat cage and limited wheel time or no wheel at all just other toys.
You should not attempt to hand rear these babies as it is a full time job and it is not just a case of feeding as you need to maintain a constant temp and also feed every few hours all night, wee and poop them and clean them up. It is a major undertaking.
If you take the pups out that have three legs mum will not take them back and she may possibly cull them or the whole litter. This is natural as mother always knows best and knows that something is wrong. The pup with the healed stump should be fine but I have my concerns about the other one as it sounds as if he has an infection in the leg. Weighing up the pros and cons if this was my pup I would risk taking it to the vets. You need to put it in a box with a warm water bottle and keep handling to a mimimum. The vet may recommend that it is given rest if the infection is bad. If he thinks it could be treated then when you take it back you need to rub it all over with bedding, even from the wee corner then occupy all the babies with food whilst you slip it back in.
Your babies are nearly ready for handling, when the eyes open, so you are close with them to make this less risky.
Here is a link to what you should be feeding the babies and the care you can give.
Good luck
Breeding Syrian Hamsters - Advice & Guidance