Babies can be handled for short bursts of time from the first day, provided they are healthy and doing well, of course. Best have them in a little cosy so they cannot suddenly wiggle and jump and always take them back as soon as mummy is not worried. Don't hold them for longer than they like. I am sure that you are allowing cuddling only under supervision, anyway!
If you can build a little baby-safe indoors run, your children will have LOTS of fun watching the babies discover the world with toilet rolls, small hurdles made from rulers, cardboard boxes, old towels etc. and lots of mad racing and popcorning once they are a few days old.
At which point have you separated the adults? If mummy has been with daddy until after the birth, you may have to brace yourself for another round of babies. Sows come into season within hours of giving birth in order to make up for the long pregnancies.