My kids always carried their own and we liked it that way so the kids could change up who they sit with without figuring out "who has the coloring books" and "where are dd's snacks". They also knew what they had with them and could help themselves.
Going through security is going to take longer with kids and stuff just relax and don't worry. The kids will feed off your stress - just do your best and it will be fine.
Do some plannning and make sure they don't have any liquids or gels - you and dh should have them all with you in your 3-1-1 bags. You can have one for each person but I usually put them all in the bin.
Plan for jackets and shoes to be removed, slipon or velcro shoes are ideal and prepare the kids for the procedure. Send one parent through the metal detector first, then the kids, then the second parent, this way the kids have someone to walk to and supervise them once they clear. Then just gather all your stuff - work swiftly as you can but don't panic.
I find using a bright unusually colored peice of ribbon on all the carryon bags, your stroller and your carseat helps. This way both DH and I know to grab everything with the purple and brown polka dot ribbon on it
I use a rolling carryon and if the kids get tired of hauling the backpack I can just clip it on to my carryon for a while.
Ok sorry way more info than you asked for - but yes to answer your OP.
FWIW the TSA website has a good section on preparing kids for travel including going through security.
TJ