I'm an academic and if you came to me with the circumstances I would absolutely be sympathetic and want to help you get through. University support services are there to help. Please see your supervisor and explain your situation. Off the top of my head, these sorts of help should be available to you:
Pastoral care - get referred or self-refer to the university counselling services. Mine has traditional one-to-one appointments as well as support groups for postgrad research students. We even have mindfulness and meditation sessions.
Academic support - what does your university have in this regard? Mine has writing tutors to advise on style, structure, expression, writing retreats (we have these for staff and I've found them surprisingly effective)
Medical allowances - if you have had a miscarriage, PTSD and you are about to have a big uptick in caring responsibilities, then there are really strong case for recognising the impact of that in some ways. When you say 'deferral' - do you men an extension of the submission deadline, or what I would call an interruption ie taking a semester or so's break? At my institution, either would be possible given what you've outlined.
Halloumiminimuffin has given some great advice on how to tackle your dissertation. Do the easy/structural stuff first and let your subconscious work away at the rest.
If you like, pm me the name of your institution and I can look into what sort of help you should be able to access.