Hi OP
I'm sorry to hear about your Mum. I tested BRCA 2 positive in 2006 (mum, sister, aunt all had BC under 40). All on the NHS, I have since had a double mastectomy. (I'm 35 now)
I think the tests have moved on a bit but back then you had to have 2 family samples to compare in order to identify the mutation (so you'd need sufficient blood samples from both you and your DM). I think it is possible now to isolate the mutation without comparable samples, but it might not be the standard test offered by the NHS (someone will correct me if I'm wrong) which may well still rely on having two samples from the same family to compare unless there is a much stronger family history.
Also, genetics is largely statistics and they have to use some criteria to judge who they select for the test, and as your DM was over 60, chances of her cancer having been genetic are massively reduced, and for anyone post-menopause, in fact.
It's also not just the expensive test, it comes with genetic counselling and potential screening even if you don't test positive. There are also other genes and "hereditary factors" that cannot be screened for and they don't fully understand yet. BRCA mutations are actually very rare, and your family history is pretty weak in comparison to many of the women I have met through BRCA networks.
The best thing to do is to keep a close eye on your breast health and request screening when you need it. But a BRCA test may not help you (as it can rule in or out a BRCA mutation, but not some other risk factors, genetic or otherwise).
I do think you should be given the opportunity to speak to a genetic counsellor who might be able to explain risk factors and family history better than I can. I was able to self refer to a genetics clinic, even 10 years ago - do you know where your nearest one might be?