I will be getting a Temporary Vehicle Permit for my dad online and he will have the permit on the vehicle. My question is do I need to be there will him when he crosses the border?
You do not need to accompany your father, and your vehicle, into Mexico, but you will need to document that he has your permission to take your car out of the US.
Customs and Border Protection (CBP) has treaties with Canada and Mexico to prevent the import/export of stolen vehicles.
In order to enforce these treaties, CBP Officers might ask to see documentation that the driver of a vehicle leaving or entering the U.S. is either the lawful owner or authorized driver of that vehicle.
If the car or vehicle is loaned or being brought into or taken out the United States on behalf of a friend or relative, the driver might want to have a notarized copy of a permission letter addressed to the "Officer In Charge of Customs and Border Protection" to drive the car across the border.
In addition to the TIP, he needs the vehicle registration (don't leave it in the car) and proof of insurance that is valid in Mexico. Having photocopies of these documents is a good idea. And, should you have a loan (or lease) on your car, you need an affidavit from any lien holders authorizing temporary importation.