I would be happy to be there when you are feeling down and anxious, I know what you're like'
No, she's totally missing the point here.
It's got fuck all to do with how she feels being around you when you're down.
It's about your feelings, you don't want anyone around while you're feeling down and anxious.
Any normal human being would understand that.
Either she's monumentally self absorbed or she's twisting things to try to get her own way.
You're doing the right thing by telling her no. She obviously has no respect for your boundaries, it's all about what she wants.
I have friends who are pretty self centred but I love them anyway.
Mumsnet will probably tell you she's not a friend etc etc, but beware of the shit stirrers here who see everything in black and white and will enjoy turning your life into a soap opera for their entertainment.
It's up to you if you want her to be your friend or not.
With my pushy friends, I've learnt to have strong boundaries and they're still my friends as they've come to learn to respect that even if it's not in their nature!
Try not to let it upset you. Tell her you're not enjoying her repeatedly asking you, you don't want other peopel round and definitely not her DP, as you don't feel up to it. You won't be persuaded so please can she drop it.
And if you're feelign concilliatory, ask her why she's having to move out and if there's anything else you can do to help. (Or if you can't be arseed, then don't!)