We went to the one in Bolingbrook a few weeks ago. My advice, go early! Ours started at 3, we got there around 2:15 and were already number 527 and 528. What they do is make you form a line, then you make your way to a person who asks you how many and gives you your numbers. When we went they only had the nasal mist which is the live vax. Not sure if they have the shots yet, but be aware that the nasal mist requires a second dose 21 days after the first, so you'll have to take your kids again (adults dont need a second dose). So, after you get your number, they take you into the gym where you have to fill out some screener paperwork to make sure you even qualify to get the shot (no major health concerns, no recent vax, etc). From there you wait until they call your number. I suppose you could get to this step and leave to get your kids, but I wouldn't risk it. I would imagine if they call your numbers and you aren't there, they move on and you are out of luck. After they call you, you take your form and someone looks it over to make sure you can get the vax, then it's on to another line where you wait to talk to a nurse who really screens you to make sure you qualify. Then you are taken to the nurse who gives you the vax, you get a card showing you got it and when to come back for the kids and you are done.
All in all it took us a little 2 hours total to be done, which with the number of people there wasn't bad. When we got there the line was already out the door and I was worried, but my 3 year old did good. I let him run around the gym to burn energy while we waited and I sat and talked to a nice woman. If you have any other questions, let me know. Good luck!