I did use kava for a short period while I was breastfeeding. I was experiencing anxiety issues and it was the only thing at the time that helped. My son was over a year old and only nursing a couple times a day though. I wouldn't use it while nursing a newborn or child under a year old.
Other good natural and safe remedies you may want to try is Rescue Remedy (flower essence), Calms Forte (homeopathic stress and tension formula), chamomile tea, hops, skullcap, catnip, and/or passion flower.
Other than internal remedies, you could also try aromatherapy- lavender is wonderful for stress and tension relief. Fresh flowers, especially roses, lilies, and lilacs can be very helpful. Don't forget about the wonders of bodywork- perhaps find time for a weekly massage, shiatsu, or acupuncture session.