I have a three-year-old and a one-year-old. They're as wiggly as all the other three-year-olds and one-year-olds I know. Prayer time at my house (and meals and any other time for that matter!) are not picture-perfect affairs with our heads all bowed and our eyes closed and the children sitting quietly on our laps. We have Gabriel now to where he gets to choose to sit on the couch or on one of our laps, with no toys allowed during prayer, but Faith still runs around a good bit or sits in our lap with a toy.
This Advent, we light our Advent candles at lunch time or dinnertime and sing a verse from "O Come, O Come Emmanuel" together, but it's usually a messy affair with the highlight being the kids taking turns blowing out the candles afterwards with adorable little sprays of of toddler spit.
I don't wait until the table is cleared or the living room is clean to do family prayer. I try to pray the Angelus with them before naptime, just plopping down on their beds or on the living room floor right where we are. I'm not waiting until they're older. Their precious little souls need prayer right now just as much as mine does.
I want my kids to never remember a day where they didn't thank God for their food and their blessings and their loved ones. I want them to go to God without even thinking, by instinct, when they are happy and when they are sad and when they are scared and when they need anything at all.