Indeed that is the puzzle, Charles had what can only be described as a 'palace' as a home in Birmingham and so his house in Belfast would not have been his main residence.
But I never found out if the business of Braddells brought him to Belfast and he met his wife there or through the heavy Irish presence in Birmingham he married and through a family trip back to the emerald isle, he came across the business of Braddells and things moved on from there.
It's hard to figure out but the underlying question is why would a established and professional man (fought in a war, ran a big gunmaking business and then association with the proof house) such as Charles Playfair (III) have time to buy into a small business some 400 miles away over the sea?
In case you are wondering, Charles Playfair (III) mother was Louisa Bentley, Thomas Bentley's daughter. Nothing like marrying your business partners prized possession!