is it possible for someone who is 18 years of age for their parents to press charges against someone they are seeing who is 22 years of age?
Not unless they are able to get a guardianship over him/her. Something like the Brittney Spears situation. Assuming that is just an issue of them not liking you, and not one where you are drugging their child or otherwise overcoming his/her will then the answer is that the 18 year old is an adult and can do what they want with whom they want when they want.
You as the more "mature" person in this relationship may need to ask yourself however why they have a problem with you and address that. The relationship between the 18 year old and their parent is an important one. Maybe you need to make some changes to make this relationship work for everyone. It would be a shame to take them away from their parents and not be there for them after.