The short answer is no. Homeowners insurance excludes coverage for motorized vehicles. There are obvious exceptions to this, such as lawn mowers.
The damage to your car would only be covered by your Auto policy, but only if you have “comprehensive coverage” as part of the policy. This coverage is sometimes called “other than collision”.
Under the above scenario, the deductible of your homeowner’s policy and your auto policy would apply. If both are insured with the same company, they may just apply one deductible.