Your homeowner's policy will not cover anything involved with the business unless you have a specific endorsement on the policy for an in-home business. You will want to check with your agent for your policy specifics.
This is how umbrella policies are designed to operate. Basically, an umbrella policy sits on top of your other insurance policies such as your homeowners or auto policy.
Coverage & Claims
Umbrella insurance provides additional liability coverage above and beyond what you have on your auto and homeowners policies. This protects your assets in the event that you are sued for injury or damage that you may have caused to another party for which you are liable.
If you currently own your home and/or other high value assets, it's probably a good idea to consider an umbrella policy to protect yourself in the event of a lawsuit. Deciding whether or not to purchase an umbrella policy is a judgement call, but it would provide you with additional liability coverage up to a minimum of $1million.
Umbrella insurance is intended to provide liability coverage in addition to that of your home and car insurance policies. There is no legal requirement to carry an umbrella insurance policy but many people do to better protect their assets if they were ever to be sued.