Some background info - The camshaft position sensor identifies which cylinder is on compression so the ECU knows the fuelling and ignition sequence on start-up. If the sensor fails, the crankshaft sensor can do the same job but takes a while to work out the firing sequence. Starting needs a few more turns of the starter motor but once it starts the engin will run normally
If the camshaft and crankshaft sensor signals get out of sync ( if the cambelt jumps a tooth or is set wrongly when doing a cambelt change) the engine won't run. If however the cam timing is not too far out, the engine may run ok if the cam sensor is disconnected.
Not sure about the petrol engines but on the diesel the crankshaft sensor works off a tone wheel fixed directly to the crank, This means a 'faulty' flywheel would have no effect on engine running.
I'm fairly sure the 1.4 petrol engine does not have a dual mass flywheel anyway
Things you need to check with the garage. If they disconnect the cam sensor and the engine runs better, check the main cambelt, the small belt between the camshafts and idler pulleys are all ok.
Assuming their flywheel diagnosis relates to the engine running problem, ask why they think this and post their answer on here.
Check if the engine actually has a dual mass flywheel.
Consider taking it to another garage for a second opinion
Cheers Spike