Wow, your neighbor is quite the piece of work. I agree with what several others have already told you - the biggest one is that you absolutely are not DUMB for helping her, not at all. She has just put you in a position that you have helped her to a fault.
There are people who like to take advantage of others and know how to "pick" those who are sweet, kind, and like to help. She in no way has the right to threaten you with anything at all and she most certainly does not have the right to involve your children or other family members. She has gone way over her "help me quota". She has also gone WAY beyond any courteous boundaries by calling your dad.
It seems to me that you have a couple of options:
1. You sit down and talk to her, set very clear boundaries, maybe even have them written down ahead of time - make a list of things you would be willing to do (I would suggest keeping this list to a bare minimum) - such as maybe still getting her meds for her and taking her grocery shopping with you on your schedule and when you will do them; also make sure to include a list of things that you absolutely will not do. Or you can just tell her the things you are willing to do will be the ONLY things you will do for her and absolutely nothing else. Should you decide to go with this option make sure to inform her verbally and/or in writing, that everything on the list(s) is non-negotiable. Give her a copy, keep a copy for you and remind her of that list should the need arise. You have a life, a family, and your own anxiety issues to deal with and shouldn't have to deal with hers.
2. Your other option is to cut her off completely, but make sure you inform her of this somehow - face-to-face, letter, phone call, whatever. But she needs to know in no uncertain terms that you will no longer have anything to do with her and she is to leave you and your family alone. If this doesn't work, do what you need to do to ensure she leaves you alone - phone number changed or blocked, make sure to tell your kids not to go anywhere near her property or house, tell her she is to stay off your property and if need be, get a restraining order (hopefully, it won't come to that though).
If she truly does need help with things, maybe you could speak to someone at your church, explain what has been going on and ask if they could put this woman in touch with services that could help her. There are many services available and I'm sure the church has such a list or knows where to start. The church may even have a group of people that go around the community to help others in need. At that point, you can wash your hands of this situation but still know that she can get some sort of assistance from someone else.
In my opinion, your priorities are taking care of you and your family - not her.
I hope I have helped a little bit and please let us know how things are going. This is a great place to be and this family is always willing to help if we can.
I have: Agoraphobia, Barrett's Esophagus, Bipolar Disorder, Depression, Fibromyalgia, Panic/Anxiety Disorders, Restless Leg Syndrome, Severe Acid Reflux, Sleep Apnea, and Social Anxiety
Meds: Ambien CR, Ativan, Flexeril, Lamictal, Lexapro, Neurontin, Nexium, Requip, Ritalin ER
A slip of the foot you may soon recover,
but a slip of the tongue you may never get over.