Because you’ve already logged the problem with your dealer, it should be on file as a pre-existing condition. Now that it has become worse, you need to take it back to the dealer and have it checked again. If the dealer won’t look at it for you, you need to do two things. First, have the vehicle independently assessed by a transmission specialist. Secondly, you should take the matter to Hyundai’s Australian customer service division.

The symptoms you’ve described are consistent with problems far too commonly found in dual-clutch transmissions. Shuddering and slow gear selection are far from unknown in this make and model, and Hyundai even had a software update to try to alleviate these problems. At the very least, the dealer could try the new software, but if left unchecked you could end up with a dead transmission that could cost many thousands to replace. So it’s crucial to keep the dealer and Hyundai Australia in the loop to maintain your warranty cover.

Most Hyundai engines with a rubber timing belt require belt changes every 100,000km. Stretching this interval is pushing your luck as a failed belt will destroy the rest of the engine. With that in mind, you’re already over that limit by about 10,000km, so a change sooner rather than later is in order.

The car will, indeed, drive perfectly even with an old timing belt. Until it doesn’t. At which point you have an engine bay full of junk and a big engine replacement bill coming your way.

That’s a pretty comprehensive rebuild of the fuel system, so it’s possible that something that was removed at the time has gone back on not quite the way it was. A shuddering as you slow down suggests that the idle speed is perhaps a touch low. You should be able to adjust the ide speed fairly simply, so the first thing to try is to creep it up, say, 100rpm and see if the shudder goes away.

A mechanic will be able to do this quickly and easily. If that’s not the problem, you need to go back and double check every fitting and fastener to make sure there’s no air or fuel leak that is causing the engine to develop the staggers. Were the new injector seals treated to a dollop of rubber grease before they were installed? If not, there’s a chance that fitting them may have put a small tear in the rubber seal which is now leaking.