I noticed that the original post was from 2 years ago.
It wasn't mentioned how old the nephew was. If he is a minor (between 14 and 17) and he is looking to do lawnwork and minor handyman jobs as casual after-school work; then that is a different situation than if he is in his 20s and looking to turn this into a full-time business.
As Sar-Con mentioned, coverage for casual part-time jobs such as babysitting and gardenwork can often be specifically covered under the parents' homeowners insurance policy by adding a rider.
Alternately, the homeowners of the places where the nephew will be working can provide the coverage. It is possible to include domestic labour such as maids, gardeners and maintenance workers as Additional Insureds on a homeowners policy as long as the work they do is strictly residential home maintenance type work at the insured home. If the neighbour's fence is damaged when the nephew is trimming the bushes, then that's covered. But if the homeowner also has him doing clean-up labour at his business' workshop, then that is not covered.
Workers Comp also needs to be considered. Generally, part-time yardwork and household chores while on the premises of a nonprofit, noncommercial organization is an exempted category. Of note, this exception usually prohibits the use of power-driven machinery. So, a homeowner who hires someone to operate a power lawn mower may actually be required to provide W/C cover. You would need to check the specific W/C requirements for your jurisdiction.
An alternative to W/C for covering domestic help, including minor handyman maintenance, is to add Employers Liability coverage to your home insurance policy.
Most people don't think twice about hiring the neighbour's boy to mow the lawn or run the snowblower without realizing that they could be held responsible if the boy is injured while using the HO's equipment. They equate the task with their own son or daughter doing the chore. The difference is when that young teenager gets injured, as a parent you are not going to sue yourself, but a neighbour parent will go after you if they feel you were negligent re their child getting injured while working for you.