There is all sorts of raw data available on maternity care on data.gov.uk, but I can't see anything on maternal mortality, and I suspect you won't find anything due to it not being possible to release data which refers to so few individuals (35 in 2010) without risking exposing personal data. Does this figure make you any less worried?
This also causes problems with analysing the data, if the numbers involved are small then its hard to see what is a systematic problem rather than a statistical "blip". If you don't have any training in statistics, I recommend staying away from the raw data, unless you want to end up basing your decision on misleading information.
As for "choice" in the NHS, Choose and Book limits the hospitals you can choose from generally, there is no right to choose any UK hospital, just to be given a choice between a few of the local hospitals which offer the treatment you require. So you should have only been offered a few.
I have used a hospital I wasn't registered at when worried about complications though: as I was away from home I just walked up to the local A&E and got them to refer me to the maternity unit (don't know if I should have done it that way, but I was worried and unable to contact my midwife). So no, an NHS hospital won't turn you away if you are in medical need and there. But that doesn't mean they will have your records, be where you have your antenatal scans or be where your midwife sends you for any complications.