I was just thinking while reading your post same as what
@Bikerbeth has put, maybe use second day at day care money to pay for carer at home in its place. Give you a chance so you can get chance to go out when virus settles and do stuff for few hours, maybe you could have someone come for a few hours on evening or few hours saturday or sunday afternoon one day a week, or even once a fortnight, so you, hubby and girls can go out for meal, a walk, to the pictures or something. Or even just use a few regular hours to get some work done uninterrupted, or sit in your conservatory and read a book. I remember you'd started with carer before lock down and said not having her back but maybe you could so something similar as well as the one who you're thinking of for longer periods, unless this one can do regular visits to replace 2nd day centre day too maybe?.
It is such a shame they were both there at day centre today and spoilt your mums chances of good second day, I think unless another suitable day (which doesn't seem to be) then I'd do same as you and keep to lovely lady mondays.
Mums DC sent letter today saying she can go back on wednesday next week with form to sign and send back. Mum said I'm not going at first and that she hadn't liked it, I kept smiling and just said You did like it, you used to come home full of beans talking about it, Go on give it a go again. She switched to how will I get there so I told her they send bus and mum said I can't go on a bus. I said It's not a normal bus mum it's their own special bus that picks you up here. It's not a normal bus full of the public, it's only for those going to day centre. Mum said Oh, cos I wouldn't knwo where to go, so I told her there was someone who came to door for her, its usually that lovely lass on it who chats to her and Mum said Oh good. I joked she is like royalty being picked up right at her door and dropped at door at the other end and then same on way back. I said I'm off to the centre they send a vehicle for me you know, which made her laugh. She didn't say anything else after that so I've signed form to post in morning and will go over early wednesday morning and hope I can get her off ok. She really did enjoy it before and I hope things now things are different cos of virus restrictions that she still does.
Good luck with new carer, one you saw today really does sound like a positive thing.