No shuttle service will do that - they're not 'personalized', they transport multiple parties. Even if yours is the only party in the van, they just won't. It's not policy.
For a grocery stop, you need to reserve a town car. Most include a free 30 minutes stop at one location; some only allow 15 minutes. You need to shop around for a service that offers what you need.
A taxi will stop, but you will pay for the driver's waiting time.
Why not use a grocery delivery service? The two popular ones here are www.wegoshop.com and www.gardengrocer.com, but Goodings also delivers its own stock, and there've been indications that Publix now provides the same service.
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