I have used Tiffany Towncar to pick me up at the airport and take me to the resort. It includes a 30 minute grocery stop on the way.
A few years ago, I chatted with the driver. I asked if Tiffany Towncar would take people from a Disney resort to Sea World. He said they would take people anywhere they wanted to go.
So I would think you could arrange to have them pick your husband up at the resort, take him to a grocery store, wait, and then take him back to the resort. Give them a call and ask. I don't have the number, but you can find it on their website.
If you're going to do that, and you need stuff from another type of store, you could ask about making two stops. If, for example, you wanted a particular type of sunscreen which the grocery store might not carry, you could ask them to take him to Walgreens and then the grocery store. Or make a liquor store stop, if that's something your family wants.
You can try calling other towncar companies as well. It doesn't hurt to ask. I can see an ad for
FL Tours on my screen as I write this.