I was the first grandchild on either side of my family, born into a network of grandparents, aunts, and uncles. From the time I was small, my grandparents on both sides, as well as my uncles and their then-girlfriends, would "take me off my mom's hands."
Far from this being "icky," it was amazing. I spent my infancy, toddlerhood, preschoolerhood, and young-childhood surrounded by a close group of adults who loved the hell out of me, knew me in more than a "Oh, we come over to coo at the baby now and then" kind of way. I felt safe, and well-loved, and I had access to all kinds of different experiences and social situations, all from the safety of family arms. If grandparents and extended family are available, I think it is AWESOME when they are so ready to contribute to childcare so actively.
Honestly, THAT kind of upbringing? Is probably more natural than this idealized martyrdom where Mom-and-Only-Mom have to deal with all the needs of a completely helpless and dependent baby for 3-5 years -- only to start again when the next baby is born.
As for "go on as if life hasn't changed?" It seems to me that if we look at the idealized "Natural mothers" that AP claims to base its practices on (and I could go on at length about how non-AP many truly-natural mothering practices are) -- women in more "natural" cultures? Have babies, and then go about their busienss. Yes, now there is a baby tied to their back and they are breastfeeding it -- but after a short break (often marked by isolation and a very limited diet, by the way) they're generally doing the same food-gathering, household-maintaining, community-participating things they did before.