I so hear what you are saying re day care centres, hospices and all of that and that was what initially put my dad off from going when it was suggested to him from his Macmillan nurse that he go and try them. And, the day care centre here in Dundee is attatched to the local hospice too which didn't help! My dad also equated hospice with dying and so many of our family over the years had spent their last days and weeks in that hospice and indeed my dad did as well at the end.
However, let me just say that the day care centers are not what your mum or my dad for that matter imagined they would be. I took my dad for the first just to see what he thought of it and what they offered etc as he was sceptical as you could imagine. When we got there they showed my dad around, what they did and what they got up to and he liked it so he agreed to go once a week. He ended up loving it so much that he started going twice a week. They have male only days, female only days and mixed days. They have Macmillan nurses who run the days and they take great care of everyone and they have gp's that you can see if need be. They offer a wide range of activities there, various complimentary therapies and you get fed loads too! In Dundee they had a chef that would come in and cook specially for everyone and they also got singers and other acts to come in and perform too.
My dad also used to get a reiki massage each time to help him relax and he loved that loads. I do think that your mum would enjoy it and perhaps in time you could suggest taking her yourself to see what it is like. She might enjoy the company too of people of a similar age in the same circumstances as herself.
People here on the site who know me and read my postings back in 2009 of my dads experiences of the centre would be able to vouch for how much my dad enjoyed it! I wrote quite a bit about that back in 09 if you want to search for my postings from back then. I'd put a link to them in this post but linking to old posts does not seem to work now and we all have to search ourselves for old posts etc.
My best to you and your mum,