We added a "home business" rider to our home insurance, costs us an extra $75 per year. Covers business equipment, computer, inventory and "furniture" like shelving/desks etc. We were told it was a pretty standard rider, so I'm sure that most insurance companies can add something similar to what you already have.
Of course they can however note it covers the equipment not liabiility for customers. my bookkeeper had this rider. She has a box outside the house where you can drop off papers but if we want to meet It will likely be a local resturant at times when they aren't busy. Some people go to H&R Block for tax help I go to Burger King! Deb's idea of a LLC [Limited Liability Corporation] is good but it doesn't prevent someone visiting your house from sueing BOTH you and the LLC for an accident casused by your house or grounds. The limit on a LLC is the assets of the corporation. there is no limit on the homeowner's libility.
However, anything dealing with food you will likely need other licensing from your municipality or county--the specifics vary widely in my area so I assume that is true everywhere else. No personal experience with the animal side of things, but again I'd check with your local authorities on the matter.