harassment from old neighbor

Hi,
I am not sure in which category to post this message. I wanted to have some advice on the following matter. I am a resident of a apartment in a complex owned by a very big real estate company in Washington DC. I have staying here for last 2 years.
Leaving aside last 4-5 months, police has visited my apartment atleast 4-5 times to check for a complaint lodged by my neighbor (occupied by an single old lady) for drugs usage. The officers were very nice to me and were just performing their duty but apologized for the constant inconvenience caused. They had to frequent my house late at night. The lady has been constantly complaining about us to the police, property manager, employees managing the reception desks, other old people staying in the building about the drug usage.
Everyone, I mentioned above has been highly appreciative of our patience, behavior and know about the constant trouble this lady has been trying to cause us. During past several months everyone mentioned above have stopped listening to her consistent complaining.
4-5 months back, I spoke to the old lady and tried to explain her that she can come anytime to our apartment and check that we do not use any kind of drugs, which of course none of the people have been able to detect. She started crying and said ‘she cannot sleep but was extremely sorry for her behavior’. For next couple of months things were fine.
In last 2 months, whenever she finds us alone she verbally abuses us (both me and my wife). Also during the past couple of months, she has started to bang on the wall in between her and my apartment with some solid piece. This not only causes severe noise disturbing our sleep but I am apprehensive that it might break the wall and cause some damage. Almost every morning (say in between 5am and 7am), she bangs on our main door and then runs into her apartment. Atleast on 2-3 occasions I have seen her doing that (I run to open the door). Also I am being told by the reception desk that she had been sniffing around our apartment for past several months to find drugs, which is severe blow on our privacy.
In my absence, other staff of the building have inspected my apartment. I respect her old age and I have been always told that loneliness and age is causing all that disturbing behavior in her. I have been extremely patient to all the happenings but have been deeply disturbed and mentally irritated because of it. I have written a similar letter to management of property but of no major result. They have told me that it seems that lady is having lot of mental disturbance because of which her behavior is like that. He also told they can not do anything else. I suggested the management to shift to another apartment but they said they are not going to pay for the move. I will have to make a move on my own. This I find pretty amazing. The manager also says that it is not there responsibility if someone is doing that to us. It can happen anywhere.
What I am looking for alternatives here. I am ready to pursue legal action against the company (a very big company) or the lady which ever is required? Can anybody suggest any other alternatives?
thanks