Ambrotypes were most common between 1852-1865, though I think they were supposed to have been most popular between 1854 and 1861. This is an ambrotype for sure? It’s a glass print? It appears to be so, but I just thought I’d ask for sure as tintypypes, common from about 1854 onwards into the 20th century, also flipped images and were popular during this time.
Looking at the woman’s dress and her hairstyle, I feel quite confident in saying this was taken during the 1860s. As for narrowing it down further, I’d guess probably before 1867. I’ve read that in the early half of the decade, it was more common for hairstyles to cover a woman’s ears, particularly older women who tended to have this severe part and sweeping backwards of hair. Around the middle of the decade, this fad changed and by the end of the decade it was fashionable to have the ears exposed and the hair pulled up and away from the ears. Additionally, the dresses in the latter part of the decade (starting in about 1867 or so) had a much different silhouette, more like the multi-layered and bustled style of the early 1870s. I’ve seen examples of necklaces like the one in your photograph in photos taken throughout the decade.
I’d say your woman is probably between 25-35 (giving an approximate birth range around 1830-1840, give or take a bit). The children are maybe around two and four (but don’t quote me on that as I’m not great as guessing ages of children), both probably born in the late 1850s or early 1860s.