Sorry to hear about your Mum, I am afraid my basic employment law training is now very out of date, and one of the legal people may be along later.
Unfortunately there is no legal obigation for a Company to provide compassionate leave, although most large companies do have a policy in place. (where I worked it was 10 days p.a).
Look at your contract or employment handbook to see what Rights you have, failing that ring HR and ask them.
If you draw a blank, I should think you would be pretty stressed looking after your Mum, worrying about the time off and being paid, so I don't think you would be doing anything underhand by seeing your GP on those grounds.
If you felt so inclined also tell your employers that is was being refused the compassionate leave on top of everything else that caused the stress. You may have an effect on them for others finding themselves in the same position in the future.