OP, I'm speaking to you as someone who has cared for someone in this situation, both as a carer and friend, and I have quite a different take than most on this thread. I'm going to share it and if it is not useful, dismiss it, but I do feel like there's a different way of viewing what's going on here.
First, Joan has not abandoned your mum. She's phoned every week for 6 years! Presumably, your mum can't chat to her on the phone herself, so she's chatting with your dad who was not her close friend. That speaks to Joan's investment with your mum and your family. I agree with the poster that said put her on speakerphone.
She's also visited several times. Now your dad and you don't like Joan terribly much and find her too bossy etc, and you don't like that she didn't chat with your mum or make enough eye contact. As someone who visits an old friend with similar neurological issues, I can tell you it is very hard work trying to think of things to say to someone who can't speak much or give much back. I love to see my friend, but I only visit about once every six months as I have a family, work and so on, and in truth, I can't think of anything much to say. I talk at her more or less, but I'm not sure that that's doing much for her, if I'm honest. When Joan comes, you don't like that she isn't great with people with dementia, and she might be very aware of this, and feel nervous or even distressed herself by these visits.
Friendships are odd things, and usually based on reciprocity, so showing interest, asking questions, sharing memories, and Joan was friends with your mum, not you, and not your dad even though you were around, they were the core of this friendship. That is now gone for Joan and she may feel quite lost and upset as well, just as you and your Dad do.
It's very different being a family member involved in someone's daily life, you get a way of involving the person, I've done this too. You get used to chatting about making the tea, what's on telly and so on and you get used to involving them, in a way that is very very hard to do for a one-off visit.
Finally, Joan is presumably around 81 years old herself, so her not offering to take your mum out seems reasonable to me.
The people at the daycare centre love and value your mum, but they are also paid and trained in how to involve and deal with people who are less verbal, confused and so on. You are valuable to your mum. Joan can't be what you want her to be now, but I think that's asking a huge amount of a friendship. Even if she could come and sit with her and hold her hand and chat away, that's a special type of a skill and a daily life type of a thing that probably isn't how their friendship used to be.
I think you are very cross because you want to see your mum as 'there' and her old life still around her- but it may be she isn't that fussed herself about that old life and having kind new daycare friends and some support for yourself and your lovely Dad is the way forward. I found my person with dementia liked the new people better in many ways, because they accept them how they are now, and aren't essentially grieving for the lost life and friendship they had- many friends would visit and then cry afterwards, and that's not helpful to the person necessarily.
I'm not suggesting you do anything much except have a little compassion for Joan, seeing she's given what she can as an ordinary human.