Fiz, my heart goes out to you.

First of all you must get a supporting letter from your GP to explain why you need a home assessment. You are entitled to a home assessment and ATOS cannot say that, because you aren't totally housebound, they won't give you one. I'm in the very same boat as you and if ATOS had any awareness of anxiety disorders (which they clearly don't) they would know that, because anxiety is an unpredictable and fluctuating condition (which PIP is supposed to allow for) it's quite feasible for a sufferer to be able to attend a familiar location one day but not the next, to be able to travel within your 'comfort zone', such as your home town, but find it impossible to attend an unfamiliar location - especially with the added stress of undergoing an assessment by someone who may have no expertise in mental health issues. Throw into the mix difficulties with transport and/or finding someone who can accompany you and the situation becomes a complete nightmare! I have a letter sent to my MP in 2012 from Mark Hoban, then a minister in the DWP, which clearly states that assessments can be carried out at home and I'd be happy to send that to your ATOS office if you wish.
I once wrote a letter to ATOS regarding an assessment for ESA which they insisted I attend. I told them that, while I've never suffered from paranoia, I felt that they were persecuting me (I guess they consider people with mental health issues to be easy targets) and said wild horses wouldn't drag me to that assessment centre - that, combined with Mark Hoban's letter, did the trick and a decision was subsequently made without my having to be assessed at all.
ATOS carry out PIP assessments in various parts of the country, the rest are undertaken by CAPITA who will grant a home assessment request without quibble. I'm fortunate to live in an area covered by CAPITA. I believe that MAXIMUS are responsible for ESA only and they are the ones I'm taking on for a home assessment at the present time.
Best of luck to you!