In the early hours of Tuesday morning police were called to reports of a firearms discharge at a house on Prince Edward Avenue in Oldham.
Armed officers traced the suspects to Chester where they were arrested in their car.
Two men and a woman, all in their 30s, have been arrested on suspicion of possession of a firearm with intent to cause fear. They remain in police custody for questioning.
A vehicle has also been seized and a forensic examination is underway.
Det Insp Clare Harrison from our Oldham district said: “This was a brazen attack against a family, filmed and plastered over social media. We do believe that this was targeted, with our suspects travelling from Birmingham and Cheshire, and there is no risk to the wider public.
“We share the shock and concern of local residents who are understandably alarmed by this incident, but please be reassured that we have a robust patrol plan in place and additional officers in the area. If you have any concerns, or want to speak to them, please do not hesitate; they are there for you.
“This type of behaviour is unacceptable, and I would like to remind people that they cannot take the law into their own hands. Regardless of where you live, if a crime is committed in Greater Manchester, we will use all resources available to track you down.”

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