What a nightmare for you! I once had a new neighbour move in who wanted to best buddies! I like my own space and privacy, but found myself in some situations that were difficult to get out of, as I also don't like confrontation or offending/upsetting people. In the end, she did get the message.
It does sound like she's very lonely, and clinging on to the first person she's made 'friends' with ... unfortunately, for you!
Personally, I don't think it's a good idea to be skulking around inside your own home, feeling like a prisoner, trying to avoid her, not answering the door, constantly having to make excuses, and never being able to enjoy going out into your garden. What kind of life is that? When she does call, I'd answer the door and simply tell her, 'sorry, it's not convenient right now as I'm busy with something, some other time, maybe ...' If she then goes on to say she'll pop in tomorrow, or invite you to hers, again simply say you'll have to take a raincheck, as you're busy. I wouldn't pretend you're going out, or put on your coat, or whatever, otherwise you'll end up on occasions feeling like you've got to leave the house when you don't want to! And if she invites you to her house, simply say you can't because your busy with other things, no need to elaborate.
The garden issue may be a little more difficult, the only thing you can do is either ignore her, and pretend you've not heard her (although it sounds that's unlikely to work!), or just give her quick wave and pop back inside telling her you're in the middle of something. If you're outside with hubby, give her wave, immediately turn away, and begin an in depth conversation with hubby. If she continues, go inside for a few minutes.
I think you need to be persistent, and continue to tell her you're busy, and hopefully she'll eventually get the message. If she doesn't, she's obviously very thick skinned, so, in order to save your own sanity, you'll just have to be blunt if it carries on!
Regarding the mild racism issue, like others have said, that would be an absolute deal breaker for me, and I'd have to tell her that what's she's said, I find very offensive, and it's best that she doesn't call again!