Your dog is 9 or 10 months old. The children come through the door or run across the garden, and your dog grabs a sleeve, a trouser leg, an arm. There is often no growl. There is a lot of movement.
What is usually happening
Children move fast, at low height, in short bursts, making high sounds. To an adolescent dog that is the most interesting thing in the house, and grabbing is how a dog joins in.
Usually this is arousal rather than aggression. That distinction matters for the plan, and it does not lower the priority. A mouthing dog can bruise or break skin on a child without ever intending harm.
Safety note
Get help now if there is stiffening, a hard stare, a growl, a raised lip, teeth used with a child's face, or any broken skin. That needs a veterinary examination and a qualified behaviour professional, not an article. Sudden behaviour change also warrants a veterinary check, because pain often presents as a change in behaviour.
Today: separate first, train second
Management is not giving up. Behaviour change is built with management plus reinforcement, and management is what buys you the weeks in which the training happens.
Put a baby gate between your dog and the room where the running happens. Use it every day at the two predictable flashpoints: after school and before dinner.
Trail a light 6 foot leash on your dog's harness indoors while children are moving. You pick up the leash and lead your dog away, so no child ever has to.
Teach the children one rule they can actually follow: when the dog gets busy, stand still, fold your arms, and walk to a grown-up. Stillness ends the game faster than shouting.
Give your dog something legal to hold when the children arrive home. A toy already in their mouth is a mouth that cannot grab a sleeve.
The 8 minute session, without the children
Practise this while the children are out or upstairs. Your dog cannot learn a new habit and rehearse the old one in the same 10 minutes.
Stand still with 15 small treats. Take 2 fast steps sideways, then stop. When your dog stops with you and has nothing in their mouth, feed 1 treat low down.
Build to 4 fast steps, then a jog of 3 steps. Any grab and you stop moving entirely, hands still, for 5 seconds, then start again more slowly.
Do 8 reps and stop. You are teaching that fast movement predicts food arriving at your knee, not fabric arriving in their mouth.
Two things that make it worse
Rough games where hands are the toy teach your dog that skin is in play. Use a tug toy so the target is 2 feet from anyone's arm.
Punishment is the other one. Reward-based methods are what the veterinary behaviour guidance recommends. Punishment-based approaches are associated with fear, avoidance and defensive aggression around exactly the people you are protecting.
Today's version, in one line: the gate goes up at 4pm, and the leash trails while anyone is running.