Follow the TSA 3-1-1 Rule. There are stricter limits on “wet” than “dry” food. “Moist” food=dry food. Try Moist Pouches and dehydrated food. No exception for prescription food or food for Service Dogs. Separate pet food from your bags at the check point.
To drive with Dogs or Cats to Mexico from the US or Canada, Mexico does not require a Health Certificate or Rabies Certificate. Mexico is not a high-risk Rabies country (CDC). Your Pet may be visually inspected for health at the border. Car Insurance (minimum Liability only) is required.