Hi Mattsmum, just to say l appreciate, from experience, how difficult it can be trying to help ageing parents. Re her eating properly - has she gained/lost weight, you should be able to tell by how her clothes fit rather than discussing it with her. If she is loosing weight you might suggest some fortifying meal supplements. It might be an idea to have a word with her neighbours and the charity shop, she'll probably take huge exception to this so exercise tact (although with hindsight I'd forget tact, plunge right in and ignore her indignation - but you know your mum, I don't). Often (and it's well documented on this forum) neighbours and friends have much more idea of how someone is coping/deteriorating than visiting family (sometimes because the parent can dupe the family). I'd approach a few key people your mum sees regularly (on your own), maybe to offer your phone number 'should it be necessary' to contact you. You may find they take the opportunity to voice their concerns. If they already have your number you could be 'checking they have it'.
Have you/your brother got Power of Attorney (for finance and health). If not you need to try to sort this out asap it will give you the ability to be included and help guide your mum with her future health and possible social care needs.
The change in dynamics when children become more and more responsible for the care of their parents can be quite a battle, always try to do what is right for your mum even though she might not see it that way. What l mean is, don't defer to her when you know you are right. You were right to insist on the car. I wish you all the best. My mum seemed to deteriorate quickly in her 80s but we later found out the neighbours had much earlier insight than we did.