Hi - I may or may not have insite but I felt I should post a response.
It sounds as though you are doing everything you can for your children. However, recently going through dog training (I know children aren't dogs, but here is my point). They want structure. Can you say you are providing them a structured environment?
You said the teenage boy comes home, lies about homework and slams his bedroom door. Who is Alpha (top) person here?
Rules need to be set and kept. Guidelines followed.
If you aren't keeping up with those then you can't expect your children to.
Why was your child out at 3a.m. looking for a "safe" place? Does he have a curfew? If he doesn't follow that curfew are there consequences? What are they?
Either you run the show or someone else will. I only say this for YOUR well being.
I'm praying for you and please keep posting. It helps and we are all here for you.