your posted reminded me of "marley and me" as well
Sounds like you give her a lot of exercise with the dog park and your son running with her. But its still not enough for her. She needs to be pushed more to make her work harder. Try getting her a back pack and slowly put more and more weight in it until you get to a point where she comes back in from her run and is tired. Or you can try finding some sort of cart for her to pull, same idea as the back pack. I think the back pack would be the easiest to try first.
If i were in your situation and have been dealing with her for 6 years then i wouldn't be able to give her up at her age. she is probably 7 or 8 years old now and probably doesn't have very many years left. You are all she knows and to rehome her now might be devastating for her.
try the backpack thing, hopefully it will work. just remember to gradually build up the weight so she doesn't hurt herself. good luck