Looking on Autotrader, it seems that family sized vehicles under 10 years old are either diesels or have small capacity turbocharged petrol engines
It might seem that way, but it isn't (unless you think anything under 2.0 litres is small?).
some with only 3 cylinders.
How many cylinders an engine has, has no bearing on whether or not it will be reliable. How well designed and engineered it is is what matters.
Are most of these small petrol engines bad?
Same as above but substitute how many cylinders for engine capacity.
If you want to know about a specific car, ask about a specific car. Not all are the same, you can't tar everything with the same brush based on engine capacity or cylinder count.
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