Never been there this late in the season but others should reply soon. Nor can I answer about the LLC. I don't believe you need anything for the vehicle in your name as long as you don't go much farther south. We always have the full permits as we travel everywhere.
Dogs: Need to have their shots up to date. Note that Mexico does not recognise 2 or three year rabies vaccinations. Must be one year. You should also obtain an International Health Certificate from your vet. In 12 years we have never been asked for papers for the dogs southbound and only once going north into the USA. However we have heard from people being asked very time.