There is no easy answer to whether or not a child is ready for that sort of separation. It truly depends on the child, and especially the security of the child's attachment to the substitute caregiver. Your maternal instincts seem to be telling you that your daughter isn't ready. Is it possible to find a middle ground? Could a trusted caregiver accompany you on the trip to attend to your daughter when you need to be away?
You know your son best and probably have the best sense of how a daycare situation will affect him. No two children's situations are the same, and each responds differently to new arrangements. Consistency of care is a significant issue for young babies. Babies can make attachments to caregivers in addition to their parents, but frequent changes in caregivers can keep a child from developing these attachments. You should inquire about the turnover rate for caregivers with the daycare facility.