I can comment from the viewpoint of one who has taken on a far-more-egregious Neighbor and won a ~2 year Easement Battle in order to access our 80 Acres which we were arbitrarily gated out of down a long, narrow Driveway due to pure spite. I didn't listen to the YouTube Audio, but I get the gist...
What is req'd is some solution that is a complete 'work around' an uncooperative individual. When my part-time Resident, full-time Drunk Neighbor, put up a spite Gate and let Cows in a 1.5 Acre area simply to make our passage difficult, I put in the pricy, automated, Solar-powered Gate below. I also put in the option of a buried 'Hall Effect' Sensor that opens when Vehicle Mass is over it. It might also work on Bicycles; I haven't tried it. Optional, remote-mount Keypads with changeable, multiple Codes are available. Something as simple as a Doorbell-style Pushbutton can open/close the Gate. The creative person could add a +12 VDC Automotive Relay triggered by a Headlight Beam or ???
Another solution is to separate out the functions of Human and Vehicle passage. To one side of any Gate, it's customary in the Wild West of Colorado to built a separate, narrower Manual Latch Gate with or without a stout Spring to self-close it. We also build a narrow 'v' pass-through that allows Bikes through if they're held vertically on only the rear Wheel. Putting in Rails in this 'v', as seen in the Commercial Cattle Guard below, would prevent a Dog from having a firm surface to step on, preventing escape. The 90 degree angle of this 'v' keeps a Dog from jumping through, since there's no 'line-of-sight' path through.
A commonly-used 'passive' solution is the Cattle Guard linked below. They go under a Gate, so some excavation is req'd. A stout version can be made from used RR Track or Timbers sitting on Blocks and secured. Commercial Cattle Guards can support Concrete Trucks, etc.. One trick is to bring a 1' or 2' square Frame section in on each side, over the Cattle Guard. This means the Cattle Guard has to be 4' wider than the clear space req'd. These side Fence Panels prevent a smart Dog from jumping around the edge of the Cattle Guard. Due to Cattle Guards being hard to keep one's balance on, Humans CAN use them, but it's tricky. Ideally, this would drive Humans to use the ~3' Human-sized, self-closing Gate, or the v-shaped walk through area adjacent to the Gate w/Cattle Guard under it. Depending on security needs, the Gate can be removed after the Cattle Guard is installed.
I Recycle, and recycled materials could be used to make a safe, heavy duty Cattle Guard that supports substantial weight while spending almost nothing. The trick with Dogs is to make the Cattle Guard surface out of tall, skinny material that Dogs can't get good footing on. They'll spook, and not try again. This is easier if large Truck weights don't have to be supported. We also have Ranch area solutions where there's a 1/2 Gate on one side of an opening, and a Cattle Guard on the other half. Light Vehicles drive in across the Cattle Guard. Occasional heavy Trucks open and use the Gated side, which has no Cattle Guard under it.
Going through an 'introductory' period, where the current Gate is locked w/Chain and must be opened manually, is one way to 'train' Users to use the Human Gate. This would depend on who controls the Gate in practice, and in Law.
We have often hiked to old Standing Stones in the Scottish Countryside, and we liked the Law - inverse to U.S. Law - where access must be granted to Antiquities. And, yes, we closed all Gates.
My problematic Neighbor, with 6 DUIs and on Probation from aiming a Shotgun at a Sheriff's Deputy, has 'disappeared'. He shot my direction some years ago, emptying a 10 Shot Clip as a 'warning'. I returned the favor to communicate it was useless to intimidate me. This is all that Bullies understand. He no longer bothers us. I inadvertently became some sort of local 'Hero' for finally standing up to this terrorizing SOB. Through my own Research, I found that we never did cross the Drunk Neighbor's Land; only a nice Neighbors. I acquired our Driveway from him on barter for some 'expired' Ditch Water Shares, and annexed our 'Flagpole' Driveway to our Land in perpetuity. My Title Company paid for 2 precise Surveys, and all Lawyer's Fees; 5 digits of $$$$$ expense. I reversed the 60-year-old, muddled Easement situation and now control all access. I ripped out his illegal Gate twice on RR Tie Posts dug in halfway to China, and never did go to Court. No need.
Against my upbringing, I learned that my initial, instinctive 'reasonableness' is best saved for reasonable Persons. I had to overcome my naivete that everyone can dealt with as though they're rational, and can be persuaded into 'reasonable' behavior. The Neighbor has made her position clear in the YouTube Video. The problem must be solved in a manner that makes her cooperation or attitude irrelevant.
Mighy Mule Gate Openers
Cattle Guards
by grizz » Sat Nov 19, 2011 3:51 am 
I see the hand is behind the back so he clearly is trying to not hit. Pretty sure I would not do the right thing here. Maybe some really smelly stuff that sprays if the gate doesn't close... 
or the simple expedient of a chain and lock so she cant use it at all.
