I wouldn't dream of asking to use someone else's car, unless it was an absolute emergency. And I wouldn't be happy about lending my car to anyone, other than my son/daughter. It's an absolute cheek, and she's taking you for a fool! Selling their own car, and refusing to buy another, but expects to use your spare car to go shopping?! What if she had an accident in it? Whether it was her fault or not, your policy would still go up if you had to make a claim!
I can understand that you say your husband is too soft to say no, and you probably would be yourself if she asked you ... I know I'd be the same! But, it would really annoy me after a while, and I'd probably say we've just renewed the insurance, and taken a policy which only allows yourself, and your husband to drive it.