Thanks for letting us know about your diagnoses, OP.
It's really good you're going to CBT. I'm inclined to say that weekly might be better, but if you're paying privately it's expensive, plus you have kids so might not have time. Also, perhaps compassion therapy just isn't the right fit for you? Have you spoken to your therapist about other options?
Has anyone discussed medication with you? I know a lot of people worry (probably quite rightly) about anti-depressants/anxiety meds being overprescribed, but they certainly helped me - I felt that they took the edge off both my depression and anxiety. They took a while to kick in properly though (about six weeks), so if you do go down that route, do make sure you continue with other things like the cbt.
I was MASSIVELY sceptical about it, but mindfulness exercises (specifically 'mindfulness-based stress reduction') really helped me get through worst times. I was really reluctant to try it as I thought it sounded like a fad, but I bought a book with a CD from amazon (I can dig it out and give you the name if you're interested) and it really helped. I still do some of the exercises (meditations?) now when I feel anxiety bubbling up, and it works, for me at least. It might not be your kind of thing, but I thought I'd mention it!
Also you say you don't work as you don't cope with pressure or people. Do you manage to get out of the house much (for walks/to do the shopping etc)? If so, how's your anxiety when you're out and about?