Are you sure their both female? Once a sow has given birth they can practically get pregnant again soon after as they go straight into heat. You need to make sure one isnt a boar or you'll be having the same problem again.
How long have you had your girls for? Are you sure they are both female? If one turns out to be a boar, please remove him immediately; sows come into season again within hours of giving birth.
You can handle a baby from day one for short bursts of time. Please weigh it daily for the first two weeks, and then weekly for the rest of its life. (Weighing is a very good ealry indicator of health problems).
Please make sure that mummy gets plenty of vitamin C, best in vitamin C rich veg and not as additive in the water bottle. You will also want to top up the hay with calcium rich alfalfa during the nursing period.
If your baby is a boy, you need to separate him at three weeks old, or you are running an increasing risk of in-breeding. A girl can stay with mummy and auntie.
Please check the sex's of your pigs as mummy pig getting pregnant so quickly will not be good for her so please seperate them.
If there is a boar then why not get him neutered and after 6-8 wheeks he can go back with mummy pig.