What actually works out well is to switch kids a few days so that mom has some alone time with older child and you take the baby. That way when the baby cries the whole day getting settled the older child isn't as upset by it all.

Normally the baby comes for drop offs and pickups and all the kids rush over to them so they are bombarded by the kids from the get go. As the time gets closer sometimes the mom will come early to pick up and come in and let baby out on the floor to crawl around and then stays till other kids start going home then goes too. That seems to work the best for me.