My 03 Hyundai sonata 2.7 v6 gets stuck in 3RE gear how do I fix it

SOURCE: Does the 2006 Hyundai Sonata

My dealership informed me that the V6 3.3 litre engine has a timing change. It is not subject to 100,000 kms change.

SOURCE: overdrive solenoid

its not that hard to fix, i did it my self on 3000gt.

SOURCE: key is stuck in ignition in 2007 hyundai sonata

The problem is in the tumbler(s) inside the assembly. Before you do anything, try penetrating oil to see if that works... otherwise, the entire assembly will need to be replaced.

SOURCE: how to change spark plugs in a 2.7 v6 hyundai

the rear plugs can only be accessed by removing the fuel/air intake plenum. If you're not familiar with the procedure, you might want to pay a mechanic to do it right.

SOURCE: hyundai sonata 2003 v6 what do i need for a tune

A tune up is generic. i don'y have specific part numbers or anything, but a tune-up generally consists of:
Spark Plug replacement (6 of them)
Spark Plug Wire replacement (6 of them)
Fuel filter replacement
Air filter replacement
On older vehicle, one would check all the components that involve spark, such as distributor cap & rotor. You might not have these, yours may be computerized, no service required until it fails.
A tune up would also include a review of all recommended service items as noted in your owners manual. Some of these might be mileage related. Such as, timing belt & transmission fluid replacement.
I normally do not do tune-up's unless the vehicle is having a problem. If you end up taking your vehicle to a mechanic to diagnose a problem, he will suggest many of these items before beginning his diagnosis.