Hi Summer, you could contact the people at Kings College London who offer a Health Psychology Service for people with dental anxiety. You can find contact e-mails and phone numbers on the link below. I don't know if they do domiciliary visits, but considering that dental phobia appears to be more common in people with agoraphobia, I would expect they do (or at least they may be able to tell you who does). Here's the link:
About King's College London : News and What's On : King's College London
I hope they will be able to help you. You can also find more information about special needs services (which in many areas includes agoraphobia) on this page:
Where can people with special needs get dental treatment?
Wishing you all the best and I hope you'll be successful with your search
!!!