As an autism mom, I'm grateful for grocery stores that do home grocery delivery. When I don't have someone to watch my kids and have to go grocery shopping, the LAST thing I want to do is take them with me. I discovered grocery delivery by accident. One week I was short on food and payday was a few days away. I asked my sister if she could wire me some money to help me get groceries. She looked online for me and found that Von's (a grocery chain in California) did home delivery for a $10 fee. She was able to pay for the groceries from her home in the midwest, and then they delivered them to my home here in CA. I was absolutely amazed that this option was available.
I have used the home-delivery service with Vons (Safeway Foods) often since then. It was a staple for us when my husband was deployed.
This is a good website to find stores in your area that do home delivery: