Yes you can, just keep in mind that the oath is kind of boring for kids and if one of them freaks out, cic employees will make them leave the ceremony with an adult (you?) and they won't let them back in ("to protect the dignity of the ceremony" though banishing fussy babies and bored toddlers does not seem dignified to me personally...)
But, your kids are on the older side, so it's probably fine. Bring toys/books/distractions because the ceremony takes a couple hours (it's mostly waiting around). If you're worried about them freaking out, make sure there's another trusted adult there to leave the room with them so you can still take your oath!
And finally, congratulations!