How can I press neglect charges on my nephew for refusing to run errands for my bedridden aunt?

Do you have a caregiver agreement in place with your nephew?

You can't obligate him to run errands unless there is a contract.

As a Human Resource Manager, I'm sure there is an employment contract, correct?

In addition to the caregiver agreement that has been mentioned I have a question.
There are errands and there are errands.
Refusing to go get an ice cream cone at the DQ at 9:30 at night is one thing, refusing to go get a medication that has bee prescribed by a doctor is another.
Refusing or delaying a medication can mean the difference between a rapid recovery or a delayed one. Refusing or delaying getting an ice cream cone is not quite as important.
How can you press charges? You don't, you terminate the employment based upon him not doing the work that was contracted. (you do have a contract right?)
If he caused bodily harm by not running an errand then you might be able to report him to the State's Elder Abuse hotline but if you have terminated the employment then you have solved the problem and the "abuse" will stop.

If your employer told you that they were paying dmv license fees to get their workers to run errands on their own time, you and probably any decent hr manager would tell them to quit it.

You can't. Refusing to run errands doesn't equate to neglect. And even if you have a contract with your nephew, breach of that contract is a civil matter, not a criminal matter.

I'm not sure what you mean by the legal rep for your mom an aunt's insurance means. What insurance? Are you talking about a LTC policy that pays for caregiving?

I'm sorry that you paid for his license for "this reason" (I'm assuming to give him the ability to run errands). Maybe it's time to write that cost off as a loss and hire someone who is more reliable to help you help them.

I can only hope that you are more attentive to negotiating employment contracts in your work life.

Besides, as NGE points out, breach of contract is a civil and not a criminal matter. Surely you can find a better solution than threatening to press neglect charges which wouldn't stick in a million years.

How young/green is your nephew? And how exactly are you expecting him to respond? - because he sure as heck isn't going to knuckle under and start running his great aunt's errands like a good boy.

Are his parents among the hacked-off family members? Maybe they'll pay back his licence fee.

In any case, surely the important thing is to get the errands run at minimal cost and maximum efficiency. I should focus on that bit.