I truly feel for you and your daughter. I do think your daughter needs a psychologist to work with. I think she will gain a lot of peace from having someone to talk to about all this loss. I would do anything possible right now to keep her in a peaceful environment. Give her time to heal, if that is possible, so much death is such a hard thing to come back from.
Call your insurance provider and visit with them. Due to the circumstances of her life she needs a therapist.
You should be able to call your insurance and tell them:
"MY daughter is sad and I am worried about her being depressed. Her doctor blows me off and I need for her to see a therapist about this. Please tell me how I can get her in counseling and which clinic accepts this insurance".
Don't mention ADHD or any other sort of medical issue, this will only come back to the doc's opinion. Just call about depression, needing an antidepressant, and that you are worried about her. Share she is worried about being away from you, that something will happen to you or to the person she is with, that she can't cope with a classroom situation due to being bullied, etc...
Any insurance company that says your family doc has to refer a child with "symptoms" of depression and the life experiences your child has been through should also be able to give you a list of all the pediatricians they have so you can go to another one. If they require her doc to do any referral then take her to a different pediatrician. Any doc will see she needs therapy.
After she's been to the psychologist a few times talk to them about the possibility of an antidepressant. If they think this will help THEN bring up the ADHD issue with that psychologist.
Your child should only get prescription meds for mental health issues through a psychiatrist. This is something I am firm about. I will not let a general doc prescribe mental health meds to my grand-kids because a general doc is just not as qualified as a psychiatrist.
For instance, if your hubby needed a heart check would you take him to your OB/GYN? Of course not, he'd go see a cardiologist. Same thing with mental health compared to being qualified to treat childhood illnesses.
Use the "right" phrases and they will get you fixed up to see a psychologist.
She's sad, she's afraid to leave the house due to someone dying, she's afraid to visit her grandmother because she's afraid grandma will die and she'll have to get help for her.
She's suffering from so much death in her life.
She needs to go to therapy so she can have someone to help her learn skills.
She needs an antidepressant. Insist on her going to a psychiatrist for a med check/prescription.
Once you have an appointment or two with the psychiatrist bring up the ADHD evaluations. It may be that the antidepressants will help with attention and other issues you're seeing.