Can dog share work?

Hello,
My own dog, A Jack Russell Terrier, died last year aged nearly 18. Since then I did a lot of dog sitting and dog walking for neighbours and through an agency.
One dog, a four year old Miniature Schnauzer, is my favourite. I have him quite often, every six weeks for a week or so and twice had him for six weeks in a row.
The owners have now asked me if I want to keep him as they think he has a better life with me. They have three children and don't have much time for the dog, who is
alone very day until 3pm. I work from home and have enough time to go on long walks with him twice a day and he is never alone for a long time.
But my husband has been diagnosed with cancer and my job is not the safest one. I need to spend quite a lot of time to go with my husband to hospital appointments etc and also if I lose my job and need to find another one where I can't work form home, what do I do?
I love that dog so much but I think this is to much responsibility at the moment as I have no idea which way things will go.
I suggested the family to "share" the dog, by which I mean coming to an arrangement where I would have him every month for a week or so but his home would still be theirs. They think it might be too confusing for the dog. But I had him quite often anyway and he is totally fine. I am also not sure about sharing vet bills, insurance etc. Right now I buy his food when he is with me.
What do people think, would it be too confusing for the dog?
Kind regards
Claudia, by email