Hi birdpumpkin, I'd say that you visiting should be seen by your mom and dad as a really thoughtful, considerate, caring gesture and absolutely not pesty.
And it is so nice that you've realized how close you guys could be, and the kind of relationship you could be having. It sounds like they mean a lot to you. Time can go by so quickly and you look around and regret what could have been, but it's never too late!!
So don't feel anxious about your visiting/your intentions, OK??!!
You should feel really proud of/pleased with/for yourself about what you're doing/what you want to do. It is a big step you're taking, but one that can lead to so much more.........
Alison