Don't glue it, as you won't be able to remove it later to clean it or refurbish the floor.
You might try wrapping the section that goes into the floor with duct tape, making it big enough to create a friction fit to the opening that your son can't remove until he's big enough to learn not to do so.
If that doesn't work then get some screws long enough to attach it to the wood subfloor. Pre-drill the register and the floor below.
And tell your son that's where the boogey man lives.