My rabbit has 6 day old kits, is she allowed out of the hutch for exercise?

We found a surprise litter of 6 kits last week from our 2 female rabbits!! As soon as i found them i removed the one i thought was the buck, had him neutered that day and he is now in a separate hutch. My doe is only just 6 months old and has taken to motherhood so well she'd made a great nest, all 6 kits are gaining weight and mum is fine with me handling them once in the morning and once at night(1 kit is a bit of a wanderer so i have to keep finding it and putting it back in the nest). Every time i open the hutch she tries to come out, i take her out for cuddles but im just not sure if she'e allowed the free rein of the garden she is used to. Does she need to stay close to her kits?? Can she mix with the buck??